Finite Group DatabasebetaFinite Group Databasebeta| order | 1626 |
| isoclinism | isoclinic class of D271 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D271 |
| Fitting, socle, Hall | C3×C271 ⋊ C2 |
| derived, Sylow | C271 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D271 |
| commutator, cosocle, hypocenter | C271 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C271 | C2 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 274 |
| transitive degree | μt(G) = 813 |
411 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D271, C2×C3×D271, C3×C7×D271, … |
| maximal normal subgroup of | D3×D271, C2×C3×D271, C3×C7×D271, … |
| maximal quotient of | C3×Dic271, C2×C3×D271, C3×C7×D271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1626, 4);