Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23×C4 |
| direct product | C23×#1899 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C23 |
| Frattini, cosocle | C24 | C23×C23 |
| prime radical | C22×D4×C23 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G | |
378 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 378 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) = 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)(26,27)(28,29)(30,33,37,40)(31,34)(32,35)(36,39,42,43)(38,41);(28,30)(29,33,35,40)(31,36)(32,37)(34,39,41,43)(38,42);(25,27)(28,31,32,38)(29,34,35,41)(30,36,37,42)(33,39,40,43)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#8487, C23×#8488, C2×C23×#1899, … |
| maximal normal subgroup of | C23×#8487, C23×#8488, C2×C23×#1899, … |
| maximal quotient of | C23×#9080, C23×#9082, C23×#9084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 631);