Finite Group DatabasebetaFinite Group Databasebeta| order | 35828 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14583752⋊C13 |
| Fitting, socle, derived | C13×C53 ⋊ C4×C13 |
| Hall | C13×C53⋊C13 ⋊ C4 |
| Sylow | C53 ⋊ C13×#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C53 | C4×C13 |
| prime radical | C13⋊(D53⋊C13) | C2 |
| cosocle | D689 | C2×C13 |
| LCS | G ▷ C13×C53 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 689 |
Polycyclic presentation:
2,13,2,13,53|a^2=c,d^a=d^5,e^a=e^30,e^b=e^16,d^c=d^12,e^c=e^52104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35828, 33);