Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊(C3⋊D9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C33 |
| direct product | C4×C3⋊(C3⋊D9) |
| Fitting | C32×C4×C9 ⋊ C2 |
| derived, Sylow | C32×C9 ⋊ C2×C4 |
400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #13047633, #13047634, #13047637, … |
| maximal normal subgroup of | #13047633, #13047634, #13047637, … |
| maximal quotient of | C8×C3⋊(C3⋊D9), #13047999, C4×C3⋊(C3⋊Dic9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 505);