Finite Group Databasebeta

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C5×#10612012 #72223402

order3200
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#10612012

Splittings

FittingC52×#453 ⋊ C2
SylowC52 ⋊ #3291

Subgroups

subgroupG/H
centerC2×C5#65924
commutator, cosocleC2×C4×C5C24×C5
FrattiniC2×C4C23×C5×D5
FittingC52×#453C2
socleC2×C52D42
hypercenterC5×#453D5
hypocenterC5C5×#3291
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#453

1088 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72223411
maximal normal subgroup of#72223411

GAP

Past the SmallGroups library coverage — no SmallGroups id.