Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #564⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×C3×#564⋊C3 |
| unambiguous semidirect product | (C2×#564)⋊C32 |
| unambiguous semidirect product | (C2×C3×#564)⋊C3 |
| Fitting | C2×C3×#564 ⋊ C3 |
| derived | #564 ⋊ C2×C32 |
| Sylow | C2×#564 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #564⋊C3 |
| commutator, cosocle, hypocenter | #564 | C2×C32 |
| Frattini | C22 | C2×C3×C22⋊A4 |
| Fitting | C2×C3×#564 | C3 |
| socle | C23×C3 | C22⋊A4 |
| LCS | G ▷ #564 | |
| UCS | C1 ◁ C2×C3 | |
384 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153853);