Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C32×#2621 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C32 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C32 |
| prime radical | C24×C32 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
1584 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 576 |
A minimal faithful permutation representation — 4 generators on 30 points:
(1,2,3)(11,12,13,14)(16,20)(21,23)(22,28)(29,30);(4,5,6)(8,10)(15,16)(17,23)(18,22)(19,20)(21,25)(24,30)(26,29)(27,28);(7,8)(9,10)(11,12)(13,14)(15,17,19,25)(16,21,20,23)(18,26,27,24)(22,30,28,29);(15,18,19,27)(16,22,20,28)(17,24,25,26)(21,29,23,30)288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 3681);