Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C4 |
| direct product | C23×#1922 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C2×D4 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| socle | C22×C23 | C4×D4 |
| prime radical | C23×C23 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C22×C8×C23 ◁ G | |
186 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 186 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) = 47 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 3 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)(32,33,36,40,37,35,44,39)(34,38,42,46,43,41,47,45);(25,28)(29,31)(32,34,36,42,37,43,44,47)(33,38,40,46,35,41,39,45);(24,26,27,30)(25,29,28,31)(32,35)(33,37)(34,41)(36,39)(38,43)(40,44)(42,45)(46,47)874 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#1922, C23×#21041, C23×#21042, … |
| maximal normal subgroup of | C2×C23×#1922, C23×#21041, C23×#21042, … |
| maximal quotient of | C23×#9533, C23×#9534, C23×#9535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 654);