Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C2 |
| direct product | #67×C27 |
| Fitting | C22×C3×C27 ⋊ C2 |
| Sylow | C3×C27 ⋊ D4 |
79 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
243 conjugacy classes — view the full character table.
| maximal subgroup of | #13047177, #13047181, #67×D27, … |
| maximal normal subgroup of | #13047177, #13047181, #67×D27, … |
| maximal quotient of | C27×Dic3⋊C4, C27×(C2×D3)⋊C4, C27×#213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 155);