Finite Group Databasebeta

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AGL(1,𝔽5)×#12687 #72242736

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

Aliases

direct productAGL(1,𝔽5)×#12687

Splittings

FittingC5×#12687 ⋊ C4
SylowC5 ⋊ C4×#12687

Subgroups

subgroupG/H
centerC22C2×AGL(1,𝔽5)×#99
commutatorC24×C5C22×C42
FrattiniC22×D4C23×AGL(1,𝔽5)
FittingC5×#12687C4
socleC22×C5C2×C4×#99
prime radicalC22×D5×#120C22
cosocleC22×D4×D5C24
hypercenter#12687AGL(1,𝔽5)
hypocenterC5C4×#12687
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ #12687

43766 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

maximal subgroup ofAGL(1,𝔽5)×#144366, AGL(1,𝔽5)×#511790
maximal normal subgroup ofAGL(1,𝔽5)×#144366, AGL(1,𝔽5)×#511790
automorphism group of#4016

GAP

Past the SmallGroups library coverage — no SmallGroups id.