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C2×C5×C4⋊(C5⋊D5) #14522911

order2000
isoclinismisoclinic class of #6045
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C23×C5

Aliases

direct productC2×C5×C4⋊(C5⋊D5)

Splittings

FittingC2×C4×C53 ⋊ C2
SylowC53 ⋊ C2×D4

Subgroups

subgroupG/H
centerC22×C5C2×C5⋊D5
commutator, cosocleC2×C52C23×C5
FrattiniC2C22×C5×C5⋊D5
FittingC2×C4×C53C2
socleC22×C53C22
hypercenterC2×C4×C5C5⋊D5
hypocenterC52C2×C5×D4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22×C5 ◁ C2×C4×C5

624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 400

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 874);