Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×D4×(C3⋊D3)⋊C3 |
| unambiguous semidirect product | (C2×D4×C3⋊D3)⋊C3 |
| Fitting | C2×D4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C22×D4 |
880 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #13140530, #13140545, #13140555, … |
| maximal normal subgroup of | #13140530, #13140545, #13140555, … |
| maximal quotient of | C2×#64087⋊C3, C2×#64094⋊C3, C2×C22⋊C4×(C3⋊D3)⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2580);