Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C32 · Schur multiplier (H2) = C28×C3 |
| direct product | C2×C32×#562 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C32 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C32 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
3456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 576 |
A minimal faithful permutation representation — 5 generators on 24 points:
(1,2)(19,20,21);(4,7)(5,9)(11,12)(13,17)(14,15)(16,18)(22,23,24);(4,7)(8,10)(12,15)(16,17);(3,4)(5,8)(6,7)(9,10)(11,13,14,18)(12,16,15,17);(3,5)(4,8)(6,9)(7,10)(11,12)(13,16)(14,15)(17,18)342 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 4587);