Finite Group Databasebeta

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AGL(1,𝔽5)×#19745 #72221604

order5120
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C8

Aliases

direct productAGL(1,𝔽5)×#19745

Splittings

FittingC5×#19745 ⋊ C4
SylowC5 ⋊ C4×#19745

Subgroups

subgroupG/H
centerC22C2×AGL(1,𝔽5)×#127
commutatorC42×C5C24×C4
FrattiniC42C24×AGL(1,𝔽5)
FittingC5×#19745C4
socleC22×C5C2×C4×#127
prime radicalD5×#19745C2
cosocleC42×D5C25
hypercenter#19745AGL(1,𝔽5)
hypocenterC5C4×#19745
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #19745

11802 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.