Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6308 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C33 |
| direct product | C22×C4⋊(C3⋊(C3⋊D3)) |
| Fitting | C22×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ C22×D4 |
3304 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11722027, C2×#11722036, #13160343, … |
| maximal normal subgroup of | C2×#11722027, C2×#11722036, #13160343, … |
| maximal quotient of | C2×#11723910, C2×C4×C4⋊(C3⋊(C3⋊D3)), C2×#11723915, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4642);