Finite Group Databasebeta

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C5×#10610434 #72223480

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

Aliases

direct productC5×#10610434

Splittings

FittingC2×C52×#100 ⋊ C2
SylowC52 ⋊ #3068

Subgroups

subgroupG/H
centerC2×C5C2×#4030
commutator, cosocleC2×C4×C5C24×C5
FrattiniC2×C4C23×C5×D5
FittingC2×C52×#100C2
socleC2×C52C2×#121
hypercenterC2×C5×#100D5
hypocenterC5C5×#3068
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C2×C5×#100

1118 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72223486
maximal normal subgroup of#72223486

GAP

Past the SmallGroups library coverage — no SmallGroups id.