Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C9 · Schur multiplier (H2) = C28 |
| direct product | C9×#3490 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C9 | C25 |
| commutator | C22 | C25×C9 |
| Frattini, socle, cosocle | C22×C3 | C25×C3 |
| prime radical | C3×#3490 | C3 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C9 ◁ G | |
1992 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 5 generators on 25 points:
(1,2,3,4,5,6,7,8,9)(10,11)(12,18)(13,17)(14,16)(15,19)(20,24)(21,23)(22,25);(10,12,14,20)(11,15,16,22)(13,19,21,25)(17,18,23,24);(11,16)(15,22)(17,23)(18,24);(12,19)(15,18)(20,25)(22,24);(11,17)(15,18)(16,23)(22,24)396 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 2222);