Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×D27 |
| Fitting | C22×C3×C27 ⋊ C2 |
| derived | C27 ⋊ C23×C3 |
| Sylow | C3×C27 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D27 |
| commutator, cosocle, hypocenter | C27 | C23×C3 |
| Frattini | C9 | C22×C3×D3 |
| Fitting | C22×C3×C27 | C2 |
| socle | C22×C32 | D9 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C22×C3 | |
143 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×D27)⋊Dic3, C3×(C2×D27)⋊C4, C2×Dic3×D27, … |
| maximal normal subgroup of | (C2×D27)⋊Dic3, C3×(C2×D27)⋊C4, C2×Dic3×D27, … |
| maximal quotient of | C2×C3×Dic54, C2×C3×C4×D27, C2×C3×D108, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 325);