Finite Group Databasebeta

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C5×#10602438 #72223413

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

Aliases

direct productC5×#10602438

Splittings

FittingC4×C52×#41 ⋊ C2
SylowC52 ⋊ #1906

Subgroups

subgroupG/H
centerC4×C5#4076
commutatorC2×C4×C5C22×C4×C5
FrattiniC22×C4C22×C5×D5
FittingC4×C52×#41C2
socleC2×C52#386
prime radicalC5×#66156C2
cosocleC22×C4×C5C23×C5
hypercenterC4×C5×#41D5
hypocenterC5C5×#1906
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C4×C5×#41

974 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72223420
maximal normal subgroup of#72223420

GAP

Past the SmallGroups library coverage — no SmallGroups id.