Finite Group DatabasebetaFinite Group Databasebeta| order | 546 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D39 |
| unambiguous semidirect product | C3⋊(C7×D13) |
| unambiguous semidirect product | C13⋊(D3×C7) |
| Fitting, socle, Hall | C3×C7×C13 ⋊ C2 |
| derived, Hall | C3×C13 ⋊ C2×C7 |
| Hall | C7×C13 ⋊ D3 |
| Hall | C3×C7 ⋊ D13 |
| Sylow | C13 ⋊ D3×C7 |
| Sylow | C3 ⋊ C7×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D39 |
| commutator, cosocle, hypocenter | C3×C13 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13 | C2 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 273 |
147 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C7×D13, D7×D39, D21⋊D13, … |
| maximal normal subgroup of | D3×C7×D13, D7×D39, D21⋊D13, … |
| maximal quotient of | C7×Dic39, C2×C7×D39, C7×D117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(546, 21);