Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | Q8×C3⋊Dic9 |
| Sylow | C3×C9 ⋊ C4×Q8 |
350 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #13140691, #13140692, #13140697, … |
| maximal normal subgroup of | #13140691, #13140692, #13140697, … |
| maximal quotient of | C4⋊C4×C3⋊Dic9, #13144326, #13144330, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1822);