Finite Group Databasebeta

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AGL(1,𝔽5)×#1619 #72258379

order2560
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productAGL(1,𝔽5)×#1619

Splittings

FittingC5×#1619 ⋊ C4
SylowC5 ⋊ C4×#1619

Subgroups

subgroupG/H
centerC22AGL(1,𝔽5)×#120
commutatorC42×C5C23×C4
FrattiniC42C23×AGL(1,𝔽5)
FittingC5×#1619C4
socleC22×C5C4×#120
prime radicalD5×#1619C2
cosocleC42×D5C24
hypercenter#1619AGL(1,𝔽5)
hypocenterC5C4×#1619
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #1619

3500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal quotient ofAGL(1,𝔽5)×#12310, AGL(1,𝔽5)×#12314

GAP

Past the SmallGroups library coverage — no SmallGroups id.