Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D3×C3⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | Dic3×C3⋊D9 |
| derived, Sylow | C32×C9 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×C3⋊D9 |
| commutator, hypocenter | C32×C9 | C2×C4 |
| Frattini | C2×C3 | D3×C3⋊D3 |
| Fitting, cosocle | C2×C32×C9 | C22 |
| socle | C2×C33 | C2×D3 |
| prime radical | C2×C3×C3⋊D9 | C2 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C2 | |
205 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×Dic3×D9, #13048287, #13048291, … |
| maximal normal subgroup of | D3×Dic3×D9, #13048287, #13048291, … |
| maximal quotient of | C3⋊C8×C3⋊D9, #13047636, Dic3×C3⋊Dic9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 390);