Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3×#560⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | D3×#560⋊C3 |
| unambiguous semidirect product | (D3×#560)⋊C3 |
| unambiguous semidirect product | ((#126⋊C3)⋊D3)⋊C2 |
| unambiguous semidirect product | (D3×#126⋊C3)⋊C2 |
| Fitting | C3×#560 ⋊ C2×C3 |
| derived | C3×C42 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C42 | C23×C3 |
| Frattini | C22 | C22×D3×A4 |
| Fitting | C3×#560 | C2×C3 |
| socle | C22×C3 | C23×A4 |
| LCS | G ▷ C3×C42 | |
| UCS | C1 | |
623 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 623 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4626⋊C2, D3×#11710731 |
| maximal normal subgroup of | D3×#4626⋊C2 |
| automorphism group of | C3⋊(#126⋊C3), C3×#126⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157307);