Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×#63357 |
| Fitting | C3×C9×C16 ⋊ C2 |
| Sylow | C3×C9 ⋊ M32 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63357, #13136961, #13136964, … |
| maximal normal subgroup of | D3×#63357, #13136961, #13136964, … |
| maximal quotient of | C3×Dic9⋊C16, C3×#10588179, C3×(C2×D9)⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 309);