Finite Group Databasebeta

← Prev (#72269473) Next (#72269475) →

AGL(1,𝔽5)×#35346 #72269474

order5120
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C216

Aliases

direct productAGL(1,𝔽5)×#35346

Splittings

FittingC5×#35346 ⋊ C4
SylowC5 ⋊ C4×#35346

Subgroups

subgroupG/H
center, FrattiniC23C25×AGL(1,𝔽5)
commutator, socleC23×C5C25×C4
FittingC5×#35346C4
prime radicalD5×#35346C2
cosocleC23×D5C26
hypercenter#35346AGL(1,𝔽5)
hypocenterC5C4×#35346
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #35346

130426 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

320 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.