Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#1861 |
| 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 | |
262 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 262 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) = 39 |
| transitive degree | μt(G) = 368 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,29,33,30,34,28,36)(26,35,32,31,38,39,37,27);(24,26,29,32,30,38,28,37)(25,31,33,39,34,27,36,35);(24,27)(25,32)(26,36)(28,39)(29,35)(30,31)(33,38)(34,37)736 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#1861, C23×#20867, C23×#21477, … |
| maximal normal subgroup of | C2×C23×#1861, C23×#20867, C23×#21477, … |
| maximal quotient of | C23×#8839, C23×#8840, C23×#8841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 593);