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C2×C4⋊(C5⋊(C5⋊D5)) #14522921

order2000
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23×C53

Aliases

direct productC2×C4⋊(C5⋊(C5⋊D5))

Splittings

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

Subgroups

subgroupG/H
centerC22C2×C5⋊(C5⋊D5)
commutator, cosocleC2×C53C23
FrattiniC2C22×C5⋊(C5⋊D5)
FittingC2×C4×C53C2
socleC22×C53C22
hypercenterC2×C4C5⋊(C5⋊D5)
hypocenterC53C2×D4
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4

1728 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1000

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 884);