Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210×C3 |
| direct product | C22×#64139 |
| Fitting | C24×C32×C4 ⋊ C2 |
| Sylow | C32 ⋊ C22×#121 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×C3⋊D3 |
| commutator, cosocle | C22×C32 | C25 |
| Frattini | C22 | C24×C3⋊D3 |
| Fitting | C24×C32×C4 | C2 |
| socle | C24×C32 | C23 |
| hypercenter | C24×C4 | C3⋊D3 |
| hypocenter | C32 | C22×#121 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C24 ◁ C24×C4 | |
7584 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134288);