Finite Group DatabasebetaFinite Group Databasebeta| order | 35217 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7×C43 · Schur multiplier (H2) = C3 |
| direct product | C3×C7×C13⋊C3×C43 |
| unambiguous semidirect product | C13⋊(C32×C7×C43) |
| unambiguous semidirect product | (C3×C13)⋊(C3×C7×C43) |
| Fitting, socle | C3×C7×C13×C43 ⋊ C3 |
| derived, Sylow | C13 ⋊ C32×C7×C43 |
| Hall | C7×C13×C43 ⋊ C32 |
| Hall | C13×C43 ⋊ C32×C7 |
| Hall | C7×C13 ⋊ C32×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7×C43 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C32×C7×C43 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C43 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C7×C43 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11739 |
6321 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35217, 41);