Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C24×C4 |
| direct product | C23×#3147 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C23 |
| socle | C22×C23 | C22×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C2×C42×C23 ◁ G | |
572 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 224 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,27)(28,29)(30,37)(31,35)(32,41)(33,36)(34,39)(38,42)(40,43);(28,30,32,39,33,40,31,38)(29,34,35,37,36,42,41,43);(24,25,26,27);(28,31,33,32)(29,35,36,41)(30,38,40,39)(34,37,42,43)1012 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#9069, C23×#9750, C23×#9753, … |
| maximal normal subgroup of | C23×#9069, C23×#9750, C23×#9753, … |
| maximal quotient of | C23×#19596, C23×#19600, C23×#19603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1879);