Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C33 |
| direct product | C3×C4×C3⋊(C3⋊D3) |
| Fitting | C34×C4 ⋊ C2 |
| derived | C33 ⋊ C2×C3×C4 |
| Sylow | C34 ⋊ C2×C4 |
682 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#88785, C3×#88788, C3⋊C8×C3⋊(C3⋊D3), … |
| maximal normal subgroup of | C3×#88785, C3×#88788, C3⋊C8×C3⋊(C3⋊D3), … |
| maximal quotient of | C3×C8×C3⋊(C3⋊D3), C3×#88850, C3×C4×C3⋊(C3⋊Dic3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 690);