Finite Group Databasebeta

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C52×#700 #14522782

order2000
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C2×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC52×#700

Splittings

SylowC53 ⋊ M16

Subgroups

subgroupG/H
centerC2×C52C2×AGL(1,𝔽5)
commutatorC2×C5C2×C4×C52
FrattiniC2C2×C52×AGL(1,𝔽5)
FittingC4×C53C4
socleC2×C53C2×C4
prime radicalC2×C52×D5C4
cosocleDic5C22×C52
hypercenterC4×C52AGL(1,𝔽5)
hypocenterC5C52×M16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C52 ◁ C4×C52

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 400

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 745);