Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C33 |
| direct product | C2×#88864 |
| Sylow | C33 ⋊ C2×C22⋊C4 |
1848 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | #13145690, #13145691, #13145692, … |
| maximal normal subgroup of | #13145690, #13145691, #13145692, … |
| maximal quotient of | C2×#11722200, #13163847, C2×#11722201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3960);