Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C23×C32×C4 ⋊ C22 |
| Sylow | C32 ⋊ #2403 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D32 |
| commutator, socle, cosocle | C23×C32 | C24 |
| Fitting | C23×C32×C4 | C22 |
| hypercenter | C23×C4 | D32 |
| hypocenter | C32 | #2403 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C23×C4 | |
3809 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|b^a=be,c^a=cf,d^a=de,i^a=hi^2,c^b=cg,h^b=h^2,i^b=i^2,h^c=h^2,i^c=i^2126 conjugacy classes — view the full character table.
| maximal subgroup of | #72214860, #72252272 |
| maximal normal subgroup of | #72214860, #72252272 |
| maximal quotient of | #72214593, #72214704, #72252291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 43025);