Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C32 · Schur multiplier (H2) = C28×C3 |
| direct product | C32×#3521 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C32 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C32 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ G | |
3126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 288 |
A minimal faithful permutation representation — 5 generators on 30 points:
(1,2,3)(8,11)(12,14)(15,16)(17,23)(18,26)(19,20)(21,25)(22,27)(24,28)(29,30);(4,5,6)(16,20)(21,23)(22,26)(28,29);(7,8)(9,12)(10,11)(13,14)(15,17,19,25)(16,21,20,23)(18,24,27,30)(22,28,26,29);(15,16)(17,21)(18,22)(19,20)(23,25)(24,28)(26,27)(29,30);(7,9,10,13)(8,12,11,14)(15,18)(16,22)(17,24)(19,27)(20,26)(21,28)(23,29)(25,30)396 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 4581);