Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6308 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C33 |
| direct product | C22×#6308 |
| Sylow | C33 ⋊ C22×Q8 |
2184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | #13160257, #13160264, C2×#11722030, … |
| maximal normal subgroup of | #13160257, #13160264, C2×#11722030, … |
| maximal quotient of | C2×C4×#6308, C2×#11723910, C2×#11723911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4640);