Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#1378 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C23 | C22⋊C4 |
| commutator | C22 | C4×C8×C23 |
| Frattini, cosocle | C22×C8 | C22×C23 |
| socle | C2×C23 | #336 |
| prime radical | C23×C23 | C2×C8 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C23 ◁ C22×C8×C23 ◁ G | |
132 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 2 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,27,31,28,33,38,45,29,32,39,44,40,46,51,54)(26,34,36,47,37,48,50,55,35,30,41,42,49,43,52,53);(24,26)(25,30,32,34)(27,36)(28,37)(29,35)(31,42,44,47)(33,43,46,48)(38,50)(39,41)(40,49)(45,53,54,55)(51,52)1012 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#1378, C23×#12597, C23×#12609, … |
| maximal normal subgroup of | C2×C23×#1378, C23×#12597, C23×#12609, … |
| maximal quotient of | C23×#7140, C23×#7144, C23×#7147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 110);