Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C211 |
| direct product | C22×C3×#953 |
| Fitting | C26×C32 ⋊ C2 |
| Sylow | C32 ⋊ C22×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C3 | C22×D3 |
| commutator, cosocle | C22×C3 | C25×C3 |
| Frattini | C22 | C24×C3×D3 |
| Fitting | C26×C32 | C2 |
| socle | C24×C32 | C23 |
| hypercenter | C26×C3 | D3 |
| hypocenter | C3 | C22×C3×#120 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C24×C3 ◁ C26×C3 | |
11913 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#10595527, C3×#11703805, C22×#64269⋊C3, … |
| maximal normal subgroup of | C22×#10595527, C3×#11703805, C3×A4×#953 |
| maximal quotient of | C3×#11661868, C22×C3×#64162 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134257);