Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2104 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×#2104 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C9 | #401 |
| commutator | C24 | C23×C9 |
| Frattini, prime radical, cosocle | C24×C3 | C23×C3 |
| socle | C2×C3 | C3×#401 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C9 ◁ C24×C9 ◁ G | |
267 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,3,4,5,6,7,8,9)(10,11)(12,18,20,15)(13,16,22,25)(14,17)(19,24)(21,23);(10,12)(11,15)(13,21,22,19)(14,20)(16,24,25,23)(17,18);(10,13)(11,16,17,25)(12,19)(14,22)(15,23,18,24)(20,21)207 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 836);