Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C23 · Schur multiplier (H2) = C23×C4 |
| direct product | C23×#1740 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C22⋊C4 |
| commutator | C22 | C2×C42×C23 |
| Frattini, cosocle | C24 | C23×C23 |
| socle | C22×C23 | C2×C22⋊C4 |
| prime radical | C24×C23 | C23 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C23×C4×C23 ◁ G | |
420 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 216 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)(28,29)(30,36,38,33)(31,34)(32,35)(37,42,43,40)(39,41);(24,25,26,27)(28,30)(29,33)(31,37)(32,38)(34,40)(35,36)(39,43)(41,42);(28,31,32,39)(29,34,35,41)(30,37,38,43)(33,40,36,42)1012 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7252, C23×#10711, C23×#10772, … |
| maximal normal subgroup of | C23×#7252, C23×#10711, C23×#10772, … |
| maximal quotient of | C23×#7906, C23×#7908, C23×#7910, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 472);