Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×((C3⋊D3)⋊C3)⋊C4 |
| derived, Sylow | H(3,𝔽3) ⋊ C23×C4 |
880 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 244 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | #13140159, #13140160, ((C3⋊D3)⋊C3)⋊#95, … |
| maximal normal subgroup of | #13140159, #13140160, ((C3⋊D3)⋊C3)⋊#95, … |
| maximal quotient of | C2×#11721053, C2×#11721055, C22×((C3⋊D3)⋊C3)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2504);