Finite Group Databasebeta

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AGL(1,𝔽5)×#10336 #72242802

order5120
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productAGL(1,𝔽5)×#10336

Splittings

FittingC5×#10336 ⋊ C4
SylowC5 ⋊ C4×#10336

Subgroups

subgroupG/H
centerC22AGL(1,𝔽5)×#392
commutatorC25×C5C23×C4
FrattiniC25C23×AGL(1,𝔽5)
FittingC5×#10336C4
socleC22×C5C4×#392
prime radicalD5×#10336C2
cosocleC25×D5C24
hypercenter#10336AGL(1,𝔽5)
hypocenterC5C4×#10336
LCSG ▷ C25×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C25 ◁ #10336

21222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

maximal quotient ofAGL(1,𝔽5)×#144366

GAP

Past the SmallGroups library coverage — no SmallGroups id.