Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#1857 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #120 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C23×C23 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G | |
272 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 272 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)(24,25,27,26)(29,33)(31,38)(34,42)(35,39)(36,40)(41,43);(24,26,27,25)(28,29)(30,34)(31,39)(32,35)(33,38)(36,41)(37,43)(40,42);(28,30,32,37)(29,34,35,43)(31,40,38,36)(33,41,39,42)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7376, C23×#12970, C23×#12971, … |
| maximal normal subgroup of | C23×#7376, C23×#12970, C23×#12971, … |
| maximal quotient of | C23×#8836, C23×#8838, C23×#8855, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 589);