Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C8 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×C32×#324 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C32 | C22⋊C4 |
| commutator | C22 | C22×C32×C8 |
| Frattini, cosocle | C22×C4 | C23×C32 |
| prime radical | C24×C32 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ C23×C32×C4 ◁ G | |
984 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 576 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2)(19,20,21);(3,4)(5,9,10,7)(6,8)(11,12,13,15,14,16,17,18)(22,23,24);(3,5,6,10)(4,7,8,9)396 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 2517);