Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1909 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C32×#1909 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | #386 |
| commutator | C2×C4 | C22×C32×C4 |
| Frattini, cosocle | C22×C4 | C23×C32 |
| prime radical | C2×C32×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ C22×C32×C4 ◁ G | |
936 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 288 |
A minimal faithful permutation representation — 3 generators on 38 points:
(1,2,3)(7,8)(9,17)(10,21,23,14)(11,24)(12,16)(13,19)(15,26)(18,31,34,38)(20,32)(22,29,25,30)(27,33,37,35)(28,36);(4,5,6)(7,9,11,19,12,20,26,36)(8,13,15,17,16,28,24,32)(10,18,25,35,23,34,22,33)(14,27,30,31,21,37,29,38);(7,10)(8,14)(9,18)(11,25)(12,23)(13,27)(15,30)(16,21)(17,31)(19,35)(20,34)(22,26)(24,29)(28,37)(32,38)(33,36)261 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 2969);