Finite Group Databasebeta

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C5×#10610717 #72223493

order3200
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#10610717

Splittings

FittingC2×C52×#104 ⋊ C2
SylowC52 ⋊ #3018

Subgroups

subgroupG/H
centerC4×C5#4028
commutator, cosocleC2×C4×C5C24×C5
FrattiniC2×C4C23×C5×D5
FittingC2×C52×#104C2
socleC2×C52C2×#120
hypercenterC2×C5×#104D5
hypocenterC5C5×#3018
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C2×C5×#104

1618 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#72223500
maximal normal subgroup of#72223500

GAP

Past the SmallGroups library coverage — no SmallGroups id.