Finite Group DatabasebetaFinite Group Databasebeta| order | 35217 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C13×C43 ⋊ C9 |
| Hall | C13×C43 ⋊ C7⋊C9 |
| Hall | C7×C43 ⋊ C13⋊C9 |
| Hall | C7×C13 ⋊ C43⋊C9 |
| Sylow | C43 ⋊ #11717941 |
| Sylow | C13 ⋊ #14582151 |
| Sylow | C7 ⋊ #19097891 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #26044070 |
| commutator, hypocenter | C7×C13×C43 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C7×C13×C43 | C3 |
| LCS | G ▷ C7×C13×C43 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 35217 |
Polycyclic presentation:
3,7,13,43,3|a^3=e,b^a=b^2,c^a=c^3,d^a=d^363921 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35217, 11);