Finite Group Databasebeta

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C5×#10605015 #72275725

order3200
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#10605015

Splittings

FittingC52×H(5,𝔽2) ⋊ C4
SylowC52 ⋊ #1792

Subgroups

subgroupG/H
centerC2×C5#65800
commutatorC2×C4×C5C22×C4×C5
FrattiniC2×C4C22×C5×AGL(1,𝔽5)
FittingC52×H(5,𝔽2)C4
socleC2×C52#379
prime radicalC5×D5×H(5,𝔽2)C2
cosocleC2×C4×D5C23×C5
hypercenterC5×H(5,𝔽2)AGL(1,𝔽5)
hypocenterC5C5×#1792
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×H(5,𝔽2)

1323 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

245 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.