Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×D3×#1009 |
| Fitting | C2×C32×#41 ⋊ C22 |
| Sylow | C32 ⋊ C22×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D32 |
| commutator, cosocle | C2×C32 | C26 |
| Frattini | C2 | C24×D32 |
| Fitting | C2×C32×#41 | C22 |
| socle | C22×C32 | C25 |
| hypercenter | C2×#41 | D32 |
| hypocenter | C32 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
13569 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D32×H(5,𝔽2), C2×D3×#4822, C2×D3×#5198 |
| maximal normal subgroup of | C2×D32×H(5,𝔽2), C2×D3×#4822, C2×D3×#5198 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153231);