Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#1855 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C2×D4 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| socle | C22×C23 | C2×C4⋊C4 |
| prime radical | C24×C23 | Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C23×C4×C23 ◁ G | |
278 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 116 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)(24,25)(26,27)(28,29,32,35,33,36,31,40)(30,37,38,34,39,42,41,43);(28,30,32,38,33,39,31,41)(29,34,35,42,36,43,40,37);(25,27)874 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#8859, C23×#8860, C23×#8874, … |
| maximal normal subgroup of | C23×#8859, C23×#8860, C23×#8874, … |
| maximal quotient of | C23×#8829, C23×#8830, C23×#8831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 587);