Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C82⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C8 |
| direct product | C2×C3×C82⋊C3 |
| unambiguous semidirect product | (C2×C82)⋊C32 |
| unambiguous semidirect product | (C2×C3×C82)⋊C3 |
| Fitting | C2×C3×C82 ⋊ C3 |
| derived | C82 ⋊ C2×C32 |
| Sylow | C2×C82 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C82⋊C3 |
| commutator, cosocle, hypocenter | C82 | C2×C32 |
| Frattini | C42 | C2×C3×A4 |
| Fitting | C2×C3×C82 | C3 |
| socle | C23×C3 | C42⋊C3 |
| LCS | G ▷ C82 | |
| UCS | C1 ◁ C2×C3 | |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153331);