Finite Group DatabasebetaFinite Group Databasebeta| order | 35217 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7×C13 · Schur multiplier (H2) = C3 |
| direct product | C32×C13×C43⋊C7 |
| unambiguous semidirect product | (C32×C43)⋊(C7×C13) |
| unambiguous semidirect product | (C32×C13×C43)⋊C7 |
| Fitting, socle, Hall | C32×C13×C43 ⋊ C7 |
| derived, Sylow | C43 ⋊ C32×C7×C13 |
| Hall | C13×C43 ⋊ C32×C7 |
| Hall | C32×C43 ⋊ C7×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C13 | C43⋊C7 |
| commutator, cosocle, hypocenter | C43 | C32×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C43 | C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C32×C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5031 |
1521 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35217, 39);