Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#798 |
| Fitting | C3×C9×C16 ⋊ C2 |
| Sylow | C3×C9 ⋊ M32 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×#798, #13136961, #13136963, … |
| maximal normal subgroup of | D9×#798, #13136961, #13136963, … |
| maximal quotient of | C9×Dic3⋊C16, C9×#4502, C9×(C2×D3)⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 314);