Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C22×C4 |
| direct product | C23×#1979 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #121 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C23×C23 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G | |
276 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 3 generators on 59 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)(28,29,33,38,34,37,32,46)(30,35,41,50,40,51,47,49)(31,42,44,52,45,56,43,36)(39,53,55,48,54,58,57,59);(24,25,26,27)(28,30,32,41,34,40,33,47)(29,35,38,49,37,51,46,50)(31,39,43,55,45,54,44,57)(36,48,42,53,52,59,56,58);(28,31,33,44,34,45,32,43)(29,36,46,56,37,52,38,42)(30,39,47,57,40,54,41,55)(35,48,50,58,51,59,49,53)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#13019, C23×#13020, C23×#13023, … |
| maximal normal subgroup of | C23×#13019, C23×#13020, C23×#13023, … |
| maximal quotient of | C23×#9669, C23×#9671, C23×#9725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 711);