Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C23×C4 |
| direct product | C23×#3135 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C23 |
| socle | C22×C23 | C22×D4 |
| prime radical | C23×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C2×C42×C23 ◁ G | |
392 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 4 generators on 47 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)(26,29)(27,28)(30,31)(32,33)(34,43)(35,39)(36,41)(37,46)(38,42)(40,45)(44,47);(25,28)(29,31)(32,34,37,35,38,45,36,44)(33,39,41,43,42,47,46,40);(24,26,27,30)(25,29,28,31)(32,35,37,45,38,44,36,34)(33,40,41,39,42,43,46,47);(32,36,38,37)(33,41,42,46)(34,44,45,35)(39,43,47,40)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#9005, C23×#9008, C23×#10033, … |
| maximal normal subgroup of | C23×#9005, C23×#9008, C23×#10033, … |
| maximal quotient of | C23×#20762, C23×#21086, C23×#21199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1867);