Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C42 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×#2110 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C8 | C42 |
| commutator | C4 | C2×C32×C42 |
| Frattini, cosocle | C2×C8 | C23×C32 |
| socle | C2×C32 | C2×#97 |
| prime radical | C23×C32 | M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C32×C8 ◁ G | |
480 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)(7,8,10,14,11,16,22,30,12,15,23,29,24,31,37,38)(9,17,19,33,20,26,35,28,18,32,21,36,34,13,25,27);(4,5,6)(7,9)(8,13,15,26)(10,21)(11,20)(12,18)(14,28,29,27)(16,17,31,32)(19,23)(22,25)(24,34)(30,36,38,33)(35,37);(9,18)(13,26)(17,32)(19,21)(20,34)(25,35)(27,28)(33,36)396 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 3170);