Finite Group Databasebeta

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C25×C22⋊AGL(1,𝔽5) #14522331

order2000
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C2×C4×C25 · Schur multiplier (H2) = C22

Aliases

direct productC25×C22⋊AGL(1,𝔽5)
unambiguous semidirect productC22⋊(AGL(1,𝔽5)×C25)
unambiguous semidirect product(C2×AGL(1,𝔽5))⋊(C2×C25)

Splittings

FittingC22×C5×C25 ⋊ C4
SylowC5×C25 ⋊ C22⋊C4

Subgroups

subgroupG/H
centerC2×C25C2×AGL(1,𝔽5)
commutatorC2×C5C2×C4×C25
FrattiniC2×C5C2×C5×AGL(1,𝔽5)
FittingC22×C5×C25C4
socleC2×C52C2×C4×C5
prime radicalC22×C5×D5C2×C5
cosocleC2×C5×D5C22×C5
hypercenterC22×C25AGL(1,𝔽5)
hypocenterC5C22⋊C4×C25
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C25 ◁ C22×C25

112 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, 294);