Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214×C3 |
| direct product | C22×#64366 |
| Fitting | C22×C32×#41 ⋊ C2 |
| Sylow | C32 ⋊ C22×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×C3⋊D3 |
| commutator, cosocle | C2×C32 | C26 |
| Frattini | C2 | C25×C3⋊D3 |
| Fitting | C22×C32×#41 | C2 |
| socle | C23×C32 | C24 |
| hypercenter | C22×#41 | C3⋊D3 |
| hypocenter | C32 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
19680 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153226);