Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C3 |
No aliases for this group.
| Fitting | C32×#568 ⋊ C2 |
| Sylow | C32 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×C3⋊D3 |
| commutator, socle | C2×C32 | C24×C4 |
| Fitting | C32×#568 | C2 |
| prime radical | #10596756 | C2 |
| cosocle | C32×C4 | C25 |
| hypercenter | #568 | C3⋊D3 |
| hypocenter | C32 | #3573 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C4 ◁ #568 | |
4272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=f,f^2=g,h^a=h^2,i^a=i^2,e^b=eg,d^c=dg,h^e=h^2,i^e=i^2204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152526);