Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C32×#2511 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C32 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C32 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
1164 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 1152 |
A minimal faithful permutation representation — 4 generators on 30 points:
(1,2,3)(8,10)(9,13)(16,19)(17,21)(23,24,27,30)(25,29,26,28);(4,5,6)(7,8,11,10)(9,14,13,12)(15,16)(17,20)(18,19)(21,22)(23,25,27,26)(24,28,30,29);(7,9,11,13)(8,12,10,14)(23,25,27,26)(24,28,30,29);(7,10,11,8)(9,14,13,12)(15,17,18,21)(16,20,19,22)(23,26,27,25)(24,29,30,28)342 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 3571);