Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C23×#334 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C23 | D4 |
| commutator | C4 | C22×C8×C23 |
| Frattini, cosocle | C42 | C23×C23 |
| socle, prime radical | C23×C23 | C4⋊C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C23 ◁ C2×C42×C23 ◁ G | |
200 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2944 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(4,7)(5,9)(8,10)(11,12,13,15,14,16,17,18);(3,4,5,7,6,8,9,10)1288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×#7156, C23×#7158, C23×#7173, … |
| maximal normal subgroup of | C23×#7156, C23×#7158, C23×#7173, … |
| maximal quotient of | C2×C23×#1277, C4×C23×#334, C23×#8595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 294);