Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #634⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C4⋊((C3⋊D3)⋊C3) |
| Fitting | C22×C4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C22×D4 |
880 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #13139944, C2×#11720308, C2×#11720318, … |
| maximal normal subgroup of | #13139944, C2×#11720308, C2×#11720318, … |
| maximal quotient of | C2×#64078⋊C3, C2×C4×C4⋊((C3⋊D3)⋊C3), C2×#11721385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2568);