7.4 Luminosity Function
The mode of formation of the Reference Catalogue prevents the
derivation of a meaningful luminosity function for groups other than
the Local Group, (Section 4) except for the very
brightest galaxies.
Table 7 gives the numbers N18
and N17 of systems with MG < -18
and MG < -17 in the B(0) system (remember that
MT is about 0.5 mag brighter on
the average) for 38 groups (including the Local Group) and 17 clouds
or clusters. The counts appear to be complete to -17 for
µ0 < 30.0
only, and to -18 for µ0 < 31.0. The average
population is 
18 = 4.3
for groups and 18
15 for clouds and clusters. On
the average a
cloud or cluster (as defined here) comprises three or four
groups. This is consistent with the ratio of average diameters
(2.5/1.5)3 and the statistical relation between volume and average
density in nearby space
(de Vaucouleurs 1960a,
1961d).
| Group | N18 | N17* |  | Range | St | n |
| 00 Local Group | 2-3 | 3-4 | +6.4 | (+3,+9) | 2.1 | 5 |
| 01 Sculptor | 3 | 4 | +7.3 | (+5,+9) | 1.0 | 6 |
| 02 M81 | 2 | 3 | +4.6 | (-1,+9) | 3.7 | 5 |
| 03 CVn I | 4 | 6 | +5.6 | (+2,+10) | 3.5 | 5 |
| 04 NGC 5128 | 3 | 6 | +3.3 | (-4,+10) | 4.7 | 6 |
| 05 M101 | 3 | 4 | +4.0 | (-1,+7) | 2.0 | 5 |
| 06 NGC 2841 | 1 | 3 | +5.8 | (0,+10) | 2.9 | 6 |
| 07 NGC 1023 | 2 | 4 | +3.8 | (-4,+7) | 3.0 | 6 |
| 08 NGC 2997 | 3 | 5 | +3.6 | (-3,+6) | 2.6 | 5 |
| 09 M66 | 3 | 4 | +1.0 | (-2,+3) | 1.6 | 5 |
| 10 CVn II | 5 | 11 | +6.0 | (+3,+9) | 2.0 | 5 |
| 11 M96 | 2 | 5 | -2.0 | (-6,+3) | 3.6 | 5 |
| 12 NGC 3184 | 4 | 4 | +6.3 | (+5,+9) | 1.4 | 4 |
| 13 Coma I | 10 | 12 | +2.0 | (-6,+5) | 3.2 | 5 |
| 14 NGC 6300 | 3 | (3) | (+4.3) | (+3,+5) | (0.9) | 3 |
| 15 Cet I | 10 | (16) | +2.8 | (-2,+5) | 1.9 | 5 |
| 16 NGC 1566 | 9 | (13) | -1.6 | (-6,+4) | 3.3 | 5 |
| 17 UMa I (Z) | 3 | (5) | +2.0 | (-3,+7) | 2.4 | 5 |
| 18 Virgo S | 27 | (45) | +3.4 | (+2,+5) | 0.9 | 5 |
| 19 Virgo E | 32 | (51) | -5.0 | (-6,-2) | 1.2 | 5 |
| 20 Virgo Y | 16 | (22) | +1.4 | (-6,+6) | 3.5 | 5 |
| 21 NGC 1433 | 8 | (8) | +1.6 | (-3,+6) | 3.5 | 5 |
| 22 NGC 1672 | 3 | (4) | +4.0 | (+3,+6) | 1.2 | 5 |
| 23 NGC 3672 | 2 | (6) | -1.5 | (-6,+5) | 3.2 | 4 |
| 24 UMa I (Y) | 3 | (6) | (+4.3) | (+3,+5) | (0.9) | 3 |
| 25 Virgo S' | 5 | (10) | +3.2 | (0,+7) | 2.2 | 5 |
| 26 Virgo X | 24 | (37) | +1.8 | (-5,+6) | 3.4 | 5 |
| 27 Grus | 17 | (24) | +1.6 | (-2,+6) | 2.1 | 5 |
| 28 UMa I (X) | 3 | (6) | +2.8 | (-3,+9) | 3.8 | 5 |
| 29 Virgo III | 15 | (23) | +3.0 | (+2,+6) | 1.6 | 5 |
| 30 NGC 5866 | 5 | (5) | +2.6 | (-2,+5) | 1.8 | 5 |
| 31 Eri | 19 | (24) | +2.2 | (-5,+5) | 3.0 | 5 |
| 32 UMa I (S) | 15 | (20) | +4.2 | (+3,+5) | 1.0 | 5 |
| 33 Cet II | 6 | (8) | -2.4 | (-6,+3) | 4.3 | 5 |
| 34 UMa I (N) | 15 | (18) | +3.2 | (+1,+5) | 1.4 | 5 |
| 35 Virgo V | 9 | (12) | +2.2 | (-4,+6) | 3.4 | 5 |
| 36 NGC 2207 | 6 | (7) | +3.4 | (-2,+6) | 2.3 | 5 |
| 37 NGC 5676 | 3 | (4) | +3.0 | (0,+5) | 1.2 | 4 |
| 38 NGC 6876 | 3 | (4) | +2.0 | (-6,+7) | 4.5 | 4 |
| 39 NGC 0134 | (5) | (5) | +0.8 | (-3,+4) | 3.0 | 5 |
| 40 NGC 0488 | 5 | (6) | +1.8 | (-3,+4) | 2.3 | 4 |
| 41 NGC 2768 | 5 | (6) | +0.8 | (-5,+7) | 4.2 | 5 |
| 42 NGC 2964 | 4 | (8) | +1.0 | (-3,+4) | 2.8 | 5 |
| 43 NGC 3396 | 3 | (3) | +4.2 | (-3,+10) | 3.4 | 5 |
| 44 NGC 3923 | 8 | (8) | -2.8 | (-6,+5) | 3.4 | 5 |
| 45 Pavo-Indus | 24 | (24) | 0.0 | (-6,+4) | 3.6 | 5 |
| 46 Virgo W | 6 | (14) | -0.2 | (-6,+5) | 3.1 | 5 |
| 47 NGC 3190 | 6 | (8) | -1.0 | (-6,+4) | 3.6 | 5 |
| 48 NGC 3504 | 3 | (3) | +0.5 | (-3,+5) | 3.0 | 4 |
| 49 NGC 3607 | 6 | (10) | -0.2 | (-6,+6) | 4.2 | 5 |
| 50 NGC 5846 | 8 | (10) | -1.8 | (-6,+3) | 3.8 | 5 |
| 51 NGC 6643 | (5) | (5) | +2.8 | (0,+5) | 2.2 | 5 |
| 52 NGC 6861 | 9 | (12) | -3.2 | (-6,0) | 1.4 | 5 |
| 53 For I | 15 | (15) | -2.6 | (-6,+4) | 2.9 | 5 |
| 54 NGC 3245 | 4 | (4) | +1.5 | (-3,+4) | 2.2 | 4 |
* Parentheses indicate incomplete data.