Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D3×#5832 |
| Fitting | C2×C32×#41 ⋊ C22 |
| Sylow | C32 ⋊ C2×#532 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Frattini | C22 | C23×D32 |
| Fitting | C2×C32×#41 | C22 |
| hypercenter | C2×#41 | D32 |
| hypocenter | C32 | C2×#532 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
3611 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#532, D3×#83937 |
| maximal normal subgroup of | D32×#532, D3×#83937 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134776);