Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#2571 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C23 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
380 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2944 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,28,26)(27,30,31,29)(33,35)(37,38)(40,41,44,47)(42,46,43,45);(25,26)(29,30)(32,33,36,35)(34,37,39,38)(40,42,44,43)(41,45,47,46);(24,26,28,25)(27,30,31,29)(32,34,36,39)(33,37,35,38)(40,41)(42,45)(43,46)(44,47);(24,27,28,31)(25,29,26,30)(32,35,36,33)(34,38,39,37)(40,43,44,42)(41,46,47,45)874 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#10351, C23×#10352, C23×#10353, … |
| maximal normal subgroup of | C23×#10351, C23×#10352, C23×#10353, … |
| maximal quotient of | C23×#13911, C23×#13982, C23×#14030, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1303);