Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C23×C32×C4 ⋊ C22 |
| Sylow | C32 ⋊ #3449 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Frattini | C22 | C23×D32 |
| Fitting | C23×C32×C4 | C22 |
| hypercenter | C23×C4 | D32 |
| hypocenter | C32 | #3449 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 | |
3557 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|e^2=f,b^a=bf,c^a=cg,d^a=df,i^a=hi^2,c^b=cf,h^b=h^2,i^b=i^2132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 135247);