Finite Group DatabasebetaFinite Group Databasebeta| order | 35828 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C169 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #6157⋊C169 |
| derived, Sylow | C53 ⋊ C4×C169 |
| Hall | C53⋊C169 ⋊ C4 |
| Hall | #6157 ⋊ C169 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C13 | AGL(1,𝔽53) |
| commutator, hypocenter | C53 | C4×C169 |
| Fitting, socle | C13×C53 | C4×C13 |
| prime radical, cosocle | C13×D53 | C2×C13 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C13 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8957 |
Polycyclic presentation:
2,13,2,53,13|a^2=c,b^13=e,d^a=d^30,d^b=d^16,d^c=d^52689 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35828, 8);