Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of (C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C4×(C3⋊D3)⋊C3 |
| Fitting | C22×C4×H(3,𝔽3) ⋊ C2 |
| derived | C32 ⋊ C23×C3×C4 |
| Sylow | H(3,𝔽3) ⋊ C23×C4 |
880 conjugacy classes of subgroups; only the 317 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 317 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #13139979, C2×#11720317, #13140024, … |
| maximal normal subgroup of | #13139979, C2×#11720317, #13140024, … |
| maximal quotient of | C2×C4×#634⋊C3, C2×C42×(C3⋊D3)⋊C3, C2×#64081⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2567);