Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C3 |
| direct product | Q8×#3830 |
| Fitting | C32×D4×Q8 ⋊ C2 |
| Sylow | C32 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×D4×Q8 | C2 |
| prime radical | C2×#3830 | C22 |
| hypercenter | D4×Q8 | C3⋊D3 |
| hypocenter | C32 | Q8×#41 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
3204 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 137744);