Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D3×D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D3×Dic27 |
| unambiguous semidirect product | (D3×C27)⋊C4 |
| derived, Sylow | C3×C27 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D27 |
| commutator, hypocenter | C3×C27 | C2×C4 |
| Frattini | C2×C9 | D32 |
| Fitting, cosocle | C2×C3×C27 | C22 |
| socle | C2×C32 | C2×D9 |
| prime radical | C2×C3×D3 | D9 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 ◁ C2 | |
73 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×Dic54, #13047102, #13047103, … |
| maximal normal subgroup of | D3×Dic54, #13047102, #13047103, … |
| maximal quotient of | D3×C27⋊C8, #13046398, Dic3×Dic27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 62);