Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #560⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×C3×#560⋊C3 |
| unambiguous semidirect product | (#126⋊C3)⋊(C22×C3) |
| unambiguous semidirect product | (C2×#560)⋊C32 |
| unambiguous semidirect product | (C2×C3×#560)⋊C3 |
| Fitting | C2×C3×#560 ⋊ C3 |
| derived | C42 ⋊ C23×C32 |
| Sylow | C2×#560 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #560⋊C3 |
| commutator, cosocle, hypocenter | C42 | C23×C32 |
| Frattini | C22 | C23×C3×A4 |
| Fitting | C2×C3×#560 | C3 |
| socle | C23×C3 | C22×A4 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C2×C3 | |
704 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×A4×#560⋊C3, C2×C3×#4626⋊C2, C2×C3×#11710731 |
| maximal normal subgroup of | C2×C3×#4626⋊C2 |
| maximal quotient of | C2×A4×#560⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153781);