Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C22×C4 |
| direct product | C23×#1977 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #121 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C22×D4×C23 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G | |
296 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 296 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)(25,27)(28,29,33,37,34,36,32,30)(31,39,41,43,42,38,40,35);(24,25,26,27)(28,30,33,36,34,37,32,29)(31,38,41,43,42,39,40,35);(28,31,32,40,34,42,33,41)(29,35,37,39,36,43,30,38)736 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#1977, C23×#21248, C23×#21249, … |
| maximal normal subgroup of | C2×C23×#1977, C23×#21248, C23×#21249, … |
| maximal quotient of | C23×#9667, C23×#9672, C23×#9723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 709);