Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C27 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic3×C27 |
| unambiguous semidirect product | (C2×C3)⋊(C4×C27) |
| derived | C3 ⋊ C2×C4×C27 |
| Sylow | C3×C27 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C27 | D3 |
| commutator, hypocenter | C3 | C2×C4×C27 |
| Frattini | C2×C9 | C2×C3×D3 |
| Fitting | C22×C3×C27 | C2 |
| socle, prime radical | C22×C32 | C2×C9 |
| cosocle | C2×C3×C9 | C22×C3 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C27 | |
79 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3×Dic27, Dic27⋊Dic3, #13046475, … |
| maximal normal subgroup of | Dic3×Dic27, Dic27⋊Dic3, #13046475, … |
| maximal quotient of | C2×C3⋊C8×C27, C27×#208, C4×Dic3×C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 153);