Finite Group Databasebeta

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C5×#64733 #13099425

order1600
isoclinismisoclinic class of #64733
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#64733

Splittings

SylowC52 ⋊ #365

Subgroups

subgroupG/H
centerC2×C5#3949
commutatorC5×C8C2×C4×C5
FrattiniC2×C8C2×C5×D5
FittingC52×M32C2
socleC2×C52#106
prime radicalC22×C52SD16
cosocleC2×C5×C8C22×C5
hypercenterC5×M32D5
hypocenterC5C5×#365
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×C8 ◁ C5×M32

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 1777);