Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C9 · Schur multiplier (H2) = C28 |
| direct product | C2×C9×#541 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C9 | C24 |
| commutator | C22 | C25×C9 |
| Frattini, cosocle | C22×C3 | C25×C3 |
| socle | C23×C3 | C24×C3 |
| prime radical | C24×C3 | C23×C3 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C9 ◁ G | |
1506 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 576 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2)(27,28,29,30,31,32,33,34,35);(5,9)(7,10)(11,12,15,18)(13,16,21,19)(14,22,23,17)(20,25,26,24);(3,4,6,8)(5,7,9,10)(11,12)(13,19)(14,17)(15,18)(16,21)(20,25)(22,23)(24,26);(3,5)(4,7)(6,9)(8,10)(11,13)(12,16)(14,20)(15,21)(17,24)(18,19)(22,25)(23,26);(11,14,15,23)(12,17,18,22)(13,20,21,26)(16,24,19,25)396 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 2185);