Finite Group DatabasebetaFinite Group Databasebeta| order | 35828 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic689⋊C13 |
| derived | C13×C53 ⋊ C4×C13 |
| Hall | C13×C53⋊C13 ⋊ C4 |
| Sylow | C53 ⋊ C13×Dic13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C13⋊(D53⋊C13) |
| commutator, hypocenter | C13×C53 | C4×C13 |
| Fitting, socle, cosocle | C2×C13×C53 | C2×C13 |
| prime radical | C2×C13×C53⋊C13 | C2 |
| LCS | G ▷ C13×C53 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2756 |
Polycyclic presentation:
2,13^2,53,2|a^2=e,c^a=c^12,d^a=d^52,d^b=d^16260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35828, 23);