Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1913 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C32×#1915 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | #386 |
| commutator | C23 | C22×C32×C4 |
| Frattini, cosocle | C22×C4 | C23×C32 |
| prime radical | C2×C32×#41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ C22×C32×C4 ◁ G | |
924 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)(7,8,11,16,12,15,17,30)(9,13,20,27,19,28,24,31)(10,21,23,32,22,14,25,29)(18,26,34,37,33,36,35,38);(4,5,6)(7,9,17,20,12,19,11,24)(8,13,16,31,15,28,30,27)(10,18,23,35,22,33,25,34)(14,26,32,37,21,36,29,38);(7,10)(8,14)(9,18)(11,25)(12,22)(13,26)(15,21)(16,32)(17,23)(19,33)(20,35)(24,34)(27,38)(28,36)(29,30)(31,37)261 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 2975);