Finite Group Databasebeta

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AGL(1,𝔽5)×#23872 #72258298

order5120
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productAGL(1,𝔽5)×#23872

Splittings

FittingC5×#23872 ⋊ C4
SylowC5 ⋊ C4×#23872

Subgroups

subgroupG/H
centerC2AGL(1,𝔽5)×#2403
commutatorC22×C4×C5C24×C4
FrattiniC22×C4C24×AGL(1,𝔽5)
FittingC5×#23872C4
socleC2×C5C4×#2403
prime radicalD5×#23872C2
cosocleC22×C4×D5C25
hypercenter#23872AGL(1,𝔽5)
hypocenterC5C4×#23872
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #23872

24978 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

holomorph ofC5×M16

GAP

Past the SmallGroups library coverage — no SmallGroups id.