Finite Group DatabasebetaFinite Group Databasebeta| order | 546 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D13⋊C3 |
| unambiguous semidirect product | D13⋊(C3×C7) |
| unambiguous semidirect product | (C13⋊C3)⋊(C2×C7) |
| Fitting, socle, Hall | C7×C13 ⋊ C2×C3 |
| derived, Sylow | C13 ⋊ C2×C3×C7 |
| Hall | C7×C13⋊C3 ⋊ C2 |
| Hall | C7×D13 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×C7 |
| Hall | D13 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13 | C2×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 91 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | C7×AGL(1,𝔽13), #11763979, D7×D13⋊C3, … |
| maximal normal subgroup of | C7×AGL(1,𝔽13), #11763979, D7×D13⋊C3, … |
| maximal quotient of | C7×Dic13⋊C3, C2×C7×D13⋊C3, C7×D13⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(546, 1);