Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #6308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C33 |
| direct product | C3×C4⋊(C3⋊(C3⋊D3)) |
| unambiguous semidirect product | C4⋊(C3×C3⋊(C3⋊D3)) |
| Fitting | C34×C4 ⋊ C2 |
| Sylow | C34 ⋊ D4 |
682 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
171 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#88790, C3×#88791, C3×#88795, … |
| maximal normal subgroup of | C3×#88790, C3×#88791, C3×#88795, … |
| maximal quotient of | C3×#88851, C3×#88852, C3×#88853, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 691);