Finite Group Databasebeta

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C5×#10604863 #72275724

order3200
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#10604863

Splittings

FittingC52×AGL(1,ℤ/8) ⋊ C4
SylowC52 ⋊ #1883

Subgroups

subgroupG/H
centerC2×C5#65779
commutatorC2×C4×C5C22×C4×C5
FrattiniC2×C4C22×C5×AGL(1,𝔽5)
FittingC52×AGL(1,ℤ/8)C4
socleC2×C52#386
prime radicalC5×D5×AGL(1,ℤ/8)C2
cosocleC2×C4×D5C23×C5
hypercenterC5×AGL(1,ℤ/8)AGL(1,𝔽5)
hypocenterC5C5×#1883
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×AGL(1,ℤ/8)

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

215 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×AGL(1,𝔽5)×#453
maximal normal subgroup ofC5×AGL(1,𝔽5)×#453

GAP

Past the SmallGroups library coverage — no SmallGroups id.