Finite Group Databasebeta

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AGL(1,𝔽5)×#8534 #72243259

order5120
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productAGL(1,𝔽5)×#8534

Splittings

FittingC5×#8534 ⋊ C4
SylowC5 ⋊ C4×#8534

Subgroups

subgroupG/H
centerC22AGL(1,𝔽5)×#379
commutatorC24×C5C22×C42
FrattiniC25C23×AGL(1,𝔽5)
FittingC5×#8534C4
socleC22×C5C4×#379
prime radicalD5×#3484C22
cosocleC25×D5C24
hypercenter#8534AGL(1,𝔽5)
hypocenterC5C4×#8534
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C25 ◁ #8534

At least 6368 conjugacy classes of subgroups; only the 748 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#347042
maximal normal subgroup ofAGL(1,𝔽5)×#347042

GAP

Past the SmallGroups library coverage — no SmallGroups id.