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C8×(C5⋊D5)⋊C5 #14522162

order2000
isoclinismisoclinic class of (C5⋊D5)⋊C5
automorphism?
homologyAbelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2×C5

Aliases

direct productC8×(C5⋊D5)⋊C5
unambiguous semidirect product(C8×C5⋊D5)⋊C5

Splittings

FittingC8×H(3,𝔽5) ⋊ C2
derivedC52 ⋊ C2×C5×C8
SylowH(3,𝔽5) ⋊ C2×C8

Subgroups

subgroupG/H
center, hypercenterC8(C5⋊D5)⋊C5
commutator, hypocenterC52C2×C5×C8
FrattiniC4×C5C2×C5×D5
FittingC8×H(3,𝔽5)C2
socleC2×C5C4×C5×D5
prime radicalC2×(C5⋊D5)⋊C5C4
cosocleC4×C52C22×C5
LCSG ▷ C52
UCSC1 ◁ C8

93 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 200

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 125);