Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C3 |
| direct product | C3⋊D3×#556 |
| Fitting | C32×#556 ⋊ C2 |
| Sylow | C32 ⋊ C2×#556 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×#556 | C2 |
| prime radical | C2×D4×C3⋊D3 | C22 |
| hypercenter | #556 | C3⋊D3 |
| hypocenter | C32 | C2×#556 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #556 | |
3336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 137359);