Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C32×#1902 |
| 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 | |
912 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)(9,18)(10,22,25,32)(11,26)(12,16)(13,17)(14,20)(15,24,31,23)(19,34,36,28)(21,29)(27,30)(33,35,38,37);(4,5,6)(7,9,11,20,13,21,12,27)(8,14,16,18,17,30,26,29)(10,19,24,37,25,36,23,35)(15,28,32,33,31,34,22,38);(7,10)(8,15)(9,19)(11,24)(12,23)(13,25)(14,28)(16,32)(17,31)(18,33)(20,37)(21,36)(22,26)(27,35)(29,38)(30,34)261 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 2962);