Finite Group Databasebeta

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C5×#10602507 #72223316

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

Aliases

direct productC5×#10602507

Splittings

SylowC52 ⋊ #1891

Subgroups

subgroupG/H
centerC4×C5#4083
commutatorC23×C5C22×C4×C5
FrattiniC22×C4C22×C5×D5
Fitting, prime radicalC52×#525C2
socleC2×C52#386
cosocleC22×C4×C5C23×C5
hypercenterC5×#525D5
hypocenterC5C5×#1891
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C5×#525

1014 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72223322
maximal normal subgroup of#72223322

GAP

Past the SmallGroups library coverage — no SmallGroups id.