Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of (C3⋊D3)⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C4×(C3⋊D3)⋊A4 |
| unambiguous semidirect product | (C4×C3⋊D3)⋊A4 |
| Fitting | C22×C32×C4 ⋊ C2×C3 |
| derived | C22×C32 ⋊ C2×C3×C4 |
328 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | ((C3⋊D3)⋊A4)⋊C8, #13146284, C8×(C3⋊D3)⋊A4, … |
| maximal normal subgroup of | ((C3⋊D3)⋊A4)⋊C8, #13146284, C8×(C3⋊D3)⋊A4, … |
| maximal quotient of | C4×#88622, #13147212, C4×#88623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2392);