Finite Group Databasebeta

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C5×#10602647 #72223331

order3200
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23×C4

Aliases

direct productC5×#10602647

Splittings

SylowC52 ⋊ #1910

Subgroups

subgroupG/H
centerC2×C5#65509
commutatorC2×C4×C5C22×C4×C5
FrattiniC22×C4C22×C5×D5
Fitting, prime radicalC52×#535C2
socleC2×C52#386
cosocleC22×C4×C5C23×C5
hypercenterC5×#535D5
hypocenterC5C5×#1910
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C5×#535

1022 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#72223337
maximal normal subgroup of#72223337

GAP

Past the SmallGroups library coverage — no SmallGroups id.