Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C3 |
No aliases for this group.
| Fitting | C22×C32×C42 ⋊ C2 |
| Sylow | C32 ⋊ #3444 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Frattini | C22 | C24×C3⋊D3 |
| Fitting | C22×C32×C42 | C2 |
| hypercenter | C22×C42 | C3⋊D3 |
| hypocenter | C32 | #3444 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C42 ◁ C22×C42 | |
3636 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|d^2=g,e^2=f,b^a=bf,c^a=cg,h^a=h^2,i^a=i^2312 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134888);