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C52×C22⋊AGL(1,𝔽5) #14522787

order2000
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C2×C4×C52 · Schur multiplier (H2) = C22×C5

Aliases

direct productC52×C22⋊AGL(1,𝔽5)
unambiguous semidirect productC22⋊(C52×AGL(1,𝔽5))
unambiguous semidirect product(C2×AGL(1,𝔽5))⋊(C2×C52)

Splittings

FittingC22×C53 ⋊ C4
SylowC53 ⋊ C22⋊C4

Subgroups

subgroupG/H
centerC2×C52C2×AGL(1,𝔽5)
commutatorC2×C5C2×C4×C52
FrattiniC2C2×C52×AGL(1,𝔽5)
FittingC22×C53C4
socleC2×C53C2×C4
prime radicalC22×C52×D5C2
cosocleC2×D5C22×C52
hypercenterC22×C52AGL(1,𝔽5)
hypocenterC5C52×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C52 ◁ C22×C52

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 200

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, 750);