Finite Group Databasebeta

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C5×#66091 #13106911

order1600
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#66091

Splittings

FittingC2×C52×D8 ⋊ C2
SylowC52 ⋊ #576

Subgroups

subgroupG/H
centerC2×C5C2×D4×D5
commutator, cosocleC4×C5C24×C5
FrattiniC4C23×C5×D5
FittingC2×C52×D8C2
socleC2×C52C22×D4
hypercenterC2×C5×D8D5
hypocenterC5C5×#576
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×D8

612 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72220877, C5×#10619093, #72221387, …
maximal normal subgroup of#72220877, C5×#10619093, #72221387, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9263);