Finite Group Databasebeta

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C5×#87810 #14522634

order2000
isoclinismisoclinic class of #87809
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C5

Aliases

direct productC5×#87810

Splittings

SylowC53 ⋊ SD16

Subgroups

subgroupG/H
centerC2×C5C22⋊(C5⋊D5)
commutator, cosocleC4×C52C22×C5
FrattiniC4C2×C5×C5⋊D5
Fitting, prime radicalC53×D4C2
socleC2×C53D4
hypercenterC5×D4C5⋊D5
hypocenterC52C5×SD16
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×D4

352 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 200

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 597);