Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#1858 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | #120 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| socle | C2×C23 | #385 |
| prime radical | C2×#41×C23 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C22×C4×C23 ◁ G | |
252 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 108 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 — 3 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)(24,25,29,33,30,34,28,41)(26,35,37,31,38,46,42,45)(27,32,39,48,40,49,43,47)(36,51,54,55,53,50,52,44);(24,26,29,37,30,38,28,42)(25,31,33,46,34,45,41,35)(27,36,39,54,40,53,43,52)(32,44,48,51,49,55,47,50);(24,27)(25,32)(26,36)(28,43)(29,39)(30,40)(31,44)(33,48)(34,49)(35,50)(37,54)(38,53)(41,47)(42,52)(45,55)(46,51)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7377, C23×#7378, C23×#12962, … |
| maximal normal subgroup of | C23×#7377, C23×#7378, C23×#12962, … |
| maximal quotient of | C23×#8835, C23×#8836, C23×#8837, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 590);