Finite Group Databasebeta

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AGL(1,𝔽5)×#87886 #72259586

order8000
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productAGL(1,𝔽5)×#87886

Splittings

FittingC22×C53 ⋊ C22×C4
SylowC53 ⋊ C2×C4×D4

Subgroups

subgroupG/H
center, FrattiniC2C2×D52×AGL(1,𝔽5)
commutator, socleC2×C53C23×C4
FittingC22×C53C22×C4
prime radicalD5×#87886C2
cosocleC2×C52×D5C24
hypercenterC22D52×AGL(1,𝔽5)
hypocenterC53C2×C4×D4
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C2 ◁ C22

2348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.