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C5×C4⋊#1044 #14522798

order2000
isoclinismisoclinic class of #87863
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2×C5

Aliases

direct productC5×C4⋊#1044
unambiguous semidirect productC4⋊(C5×#1044)

Splittings

FittingC4×C53 ⋊ C4
SylowC53 ⋊ C4⋊C4

Subgroups

subgroupG/H
centerC2×C5C2×#1044
commutatorC2×C52C2×C4×C5
FrattiniC2C2×C5×#1044
FittingC4×C53C4
socleC2×C53C2×C4
prime radicalC2×C5×C5⋊D5C22
cosocleC2×C5⋊D5C22×C5
hypercenterC4×C5#1044
hypocenterC52C5×C4⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C5 ◁ C4×C5

172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

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, 761);