Finite Group DatabasebetaFinite Group Databasebeta| order | 35217 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#26044070 |
| Fitting, socle | C3×C7×C13×C43 ⋊ C3 |
| derived, Hall | C7×C13×C43 ⋊ C32 |
| Hall | C13×C43 ⋊ C3×ΓL(1,𝔽8) |
| Hall | C7×C43 ⋊ C3×C13⋊C3 |
| Hall | C7×C13 ⋊ C3×C43⋊C3 |
| Sylow | C43 ⋊ C3×#63270 |
| Sylow | C13 ⋊ C3×#11744749 |
| Sylow | C7 ⋊ C3×#13131976 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #26044070 |
| commutator, cosocle, hypocenter | C7×C13×C43 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C43 | C3 |
| LCS | G ▷ C7×C13×C43 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11739 |
3921 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35217, 48);