Finite Group Databasebeta

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C5×C4⋊#1035 #14522318

order2000
isoclinismisoclinic class of #87735
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×C4⋊#1035
unambiguous semidirect productC4⋊(C5×#1035)

Splittings

FittingC4×C5×C25 ⋊ C4
SylowC5×C25 ⋊ C4⋊C4

Subgroups

subgroupG/H
centerC2×C5C2×#1035
commutatorC2×C25C2×C4×C5
FrattiniC2×C5C2×C5×AGL(1,𝔽5)
FittingC4×C5×C25C4
socleC2×C52C2×AGL(1,𝔽5)
prime radicalC2×C5×D25C22
cosocleC2×D25C22×C5
hypercenterC4×C5#1035
hypocenterC25C5×C4⋊C4
LCSG ▷ C2×C25 ▷ C25
UCSC1 ◁ C2×C5 ◁ C4×C5

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 400

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 281);