Finite Group Databasebeta

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C5×#10615769 #72223277

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

Aliases

direct productC5×#10615769

Splittings

FittingC23×C52×D4 ⋊ C2
SylowC52 ⋊ #3003

Subgroups

subgroupG/H
centerC22×C5C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C5
FrattiniC2×C4C23×C5×D5
FittingC23×C52×D4C2
socleC22×C52C22×D4
hypercenterC23×C5×D4D5
hypocenterC5C5×#3003
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ C23×C5×D4

3350 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72223291
maximal normal subgroup of#72223291

GAP

Past the SmallGroups library coverage — no SmallGroups id.