Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C16 · Schur multiplier (H2) = C2 |
| direct product | C9×#1400 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C9 | C22⋊C4 |
| commutator | C22 | C2×C9×C16 |
| Frattini, cosocle | C2×C3×C16 | C22×C3 |
| socle | C2×C3 | C3×C22⋊C16 |
| prime radical | C23×C3 | C3×C16 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C9 ◁ C2×C9×C16 ◁ G | |
111 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 288 |
A minimal faithful permutation representation — 2 generators on 41 points:
(1,2,3,4,5,6,7,8,9)(10,11,12,17,13,18,21,29,14,19,22,30,23,31,34,39,15,16,20,26,24,27,32,36,25,28,33,37,35,38,40,41);(11,16)(12,20)(18,27)(19,28)(21,32)(22,33)(31,38)(34,40)396 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 132);