Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C32×#2513 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C32 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C32 |
| prime radical | C22×C32×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
1320 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)(7,8,11,9)(10,13,14,12)(16,19)(17,21)(23,24,27,30)(25,29,26,28);(4,5,6)(8,9)(12,13)(15,16,18,19)(17,20,21,22)(23,25,27,26)(24,28,30,29);(7,9,11,8)(10,13,14,12)(15,16)(17,20)(18,19)(21,22)(23,24)(25,28)(26,29)(27,30);(7,10,11,14)(8,12,9,13)(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, 3573);