Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D32⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#88932 |
| Sylow | C33 ⋊ C2×C22⋊C4 |
500 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #13165370, #13165373, #13165376, … |
| maximal normal subgroup of | #13165370, #13165373, #13165376, … |
| maximal quotient of | #13166951, #13166952, C2×#11722751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4283);