Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C4×C3⋊D9 |
| Fitting | C32×C4×C9 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C3×C4 |
| Sylow | C32×C9 ⋊ C2×C4 |
205 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(C3⋊D9)⋊C8, C3×#88414, C3⋊C8×C3⋊D9, … |
| maximal normal subgroup of | C3×(C3⋊D9)⋊C8, C3×#88414, C3⋊C8×C3⋊D9, … |
| maximal quotient of | C3×C8×C3⋊D9, C3×#88523, C3×C4×C3⋊Dic9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 471);