Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #560⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C24 |
| direct product | C2×#560⋊C9 |
| unambiguous semidirect product | (C2×#560)⋊C9 |
| unambiguous semidirect product | (#126⋊C9)⋊C22 |
| derived | C42 ⋊ C23×C9 |
| Sylow | C2×#560 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #560⋊C3 |
| commutator, hypocenter | C42 | C23×C9 |
| Frattini | C22×C3 | C23×A4 |
| Fitting, prime radical | C2×C3×#560 | C3 |
| socle | C23×C3 | C22×A4 |
| cosocle | C3×C42 | C23×C3 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C2×C3 | |
560 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 84 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.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153782);