Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×C4×D27 |
| Fitting | C3×C4×C27 ⋊ C2 |
| derived | C27 ⋊ C2×C3×C4 |
| Sylow | C3×C27 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | D27 |
| commutator, hypocenter | C27 | C2×C3×C4 |
| Frattini | C2×C9 | C2×C3×D3 |
| Fitting | C3×C4×C27 | C2 |
| socle | C2×C32 | C2×D9 |
| prime radical | C2×C3×D27 | C2 |
| cosocle | C2×C27 | C22×C3 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C3×C4 | |
73 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊C8×D27, #13046392, C3×C8×D27, … |
| maximal normal subgroup of | C3⋊C8×D27, #13046392, C3×C8×D27, … |
| maximal quotient of | C3×C8×D27, C3×#88359, C3×C4×Dic27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 119);