Finite Group Databasebeta

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C5×#87804 #14522628

order2000
isoclinismisoclinic class of #6045
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C5

Aliases

direct productC5×#87804

Splittings

SylowC53 ⋊ M16

Subgroups

subgroupG/H
centerC4×C5C2×C5⋊D5
commutatorC2×C52C2×C4×C5
FrattiniC4C2×C5×C5⋊D5
FittingC2×C4×C53C2
socleC2×C53C2×C4
prime radicalC22×C53C4
cosocleC4×C52C22×C5
hypercenterC2×C4×C5C5⋊D5
hypocenterC52C5×M16
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C4×C5 ◁ C2×C4×C5

352 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 200

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, 591);