Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C3×D32⋊C4 |
| Sylow | C33 ⋊ C2×C22⋊C4 |
500 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×D32⋊C4, #13165373, #13165374, … |
| maximal normal subgroup of | Dic3×D32⋊C4, #13165373, #13165374, … |
| maximal quotient of | C3×#10593341, C3×#10593342, C2×C3×D32⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4254);