Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C2×C4 |
| direct product | C23×#1931 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #121 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C22×D4×C23 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G | |
232 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 736 |
A minimal faithful permutation representation — 3 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)(24,25,27,26)(29,33)(30,37)(31,34)(35,42)(36,40)(39,43);(24,26,27,25)(28,29,34,40,32,36,31,33)(30,35,41,42,37,43,38,39);(28,30,31,38,32,37,34,41)(29,35,33,39,36,43,40,42)736 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#1931, C23×#21075, C23×#21076, … |
| maximal normal subgroup of | C2×C23×#1931, C23×#21075, C23×#21076, … |
| maximal quotient of | C23×#9550, C23×#9552, C23×#9563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 663);