Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D4×#3673 |
| Fitting | D42×C9 ⋊ C2 |
| Sylow | C9 ⋊ D4×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×#611 |
| commutator, cosocle | C2×C4×C9 | C24 |
| Frattini | C2×C3×C4 | C23×D3 |
| Fitting | D42×C9 | C2 |
| socle | C22×C3 | C22×#67 |
| hypercenter | D42 | D9 |
| hypocenter | C9 | D4×D8 |
| LCS | G ▷ C2×C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ D42 | |
930 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 119734);