Finite Group Databasebeta

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AGL(1,𝔽5)×#511790 #72243502

order10240
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C212

Aliases

direct productAGL(1,𝔽5)×#511790

Splittings

FittingC5×#511790 ⋊ C4
SylowC5 ⋊ C4×#511790

Subgroups

subgroupG/H
centerC2AGL(1,𝔽5)×#32898
commutatorC22×C5×D4C24×C4
FrattiniC22×D4C24×AGL(1,𝔽5)
FittingC5×#511790C4
socleC2×C5C4×#32898
prime radicalD5×#511790C2
cosocleC22×D4×D5C25
hypercenter#511790AGL(1,𝔽5)
hypocenterC5C4×#511790
LCSG ▷ C22×C5×D4 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C23 ◁ C23×D4 ◁ #511790

At least 31328 conjugacy classes of subgroups; only the 1930 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

265 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽5)×AGL(2,ℤ/4)
automorphism group of#4015
holomorph ofC5×C22⋊C4

GAP

Past the SmallGroups library coverage — no SmallGroups id.