Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C9 · Schur multiplier (H2) = C23 |
| direct product | C9×#2514 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C9 | C24 |
| commutator | C23 | C24×C9 |
| Frattini, socle, prime radical, cosocle | C23×C3 | C24×C3 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C9 ◁ G | |
558 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1152 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9)(11,13)(12,16)(18,19,23,21)(20,25,24,22)(28,32)(30,33);(10,11,14,13)(12,15,16,17)(18,20)(19,22)(21,25)(23,24)(26,27,29,31)(28,33,32,30);(10,12)(11,15)(13,17)(14,16)(18,21,23,19)(20,25,24,22)(26,28,29,32)(27,30,31,33);(10,13,14,11)(12,17,16,15)(18,22,23,25)(19,24,21,20)342 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 1246);