Finite Group Databasebeta

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C5×C22⋊#1039 #14522637

order2000
isoclinismisoclinic class of #6045
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22×C5

Aliases

direct productC5×C22⋊#1039
unambiguous semidirect productC22⋊(C5×#1039)

Splittings

SylowC53 ⋊ C22⋊C4

Subgroups

subgroupG/H
centerC22×C5C2×C5⋊D5
commutatorC2×C52C2×C4×C5
FrattiniC22C2×C5×C5⋊D5
Fitting, prime radicalC23×C53C2
socleC22×C53C22
cosocleC22×C52C22×C5
hypercenterC23×C5C5⋊D5
hypocenterC52C5×C22⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22×C5 ◁ C23×C5

656 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, 600);