Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C33 |
| direct product | C4×#6308 |
| Sylow | C33 ⋊ C4×Q8 |
980 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | #13145516, #13145517, #13146009, … |
| maximal normal subgroup of | #13145516, #13145517, #13146009, … |
| maximal quotient of | #13163288, #13163292, #13163295, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3876);