Finite Group Databasebeta

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C5×#10603919 #72275723

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

Aliases

direct productC5×#10603919

Splittings

FittingC52×#99 ⋊ C4
SylowC52 ⋊ #1867

Subgroups

subgroupG/H
centerC2×C5#65699
commutatorC23×C5C22×C4×C5
FrattiniC23C22×C5×AGL(1,𝔽5)
FittingC52×#99C4
socleC2×C52#385
prime radicalC2×C5×D4×D5C22
cosocleC23×D5C23×C5
hypercenterC5×#99AGL(1,𝔽5)
hypocenterC5C5×#1867
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C23×C5 ◁ C5×#99

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)×B(4,𝔽2), #72275819
maximal normal subgroup ofC5×AGL(1,𝔽5)×B(4,𝔽2)
maximal quotient of#72275819

GAP

Past the SmallGroups library coverage — no SmallGroups id.