Finite Group Databasebeta

← Prev (#14522315) Next (#14522317) →

C25×C4⋊AGL(1,𝔽5) #14522316

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

Aliases

direct productC25×C4⋊AGL(1,𝔽5)
unambiguous semidirect productC4⋊(AGL(1,𝔽5)×C25)

Splittings

FittingC4×C5×C25 ⋊ C4
SylowC5×C25 ⋊ C4⋊C4

Subgroups

subgroupG/H
centerC2×C25C2×AGL(1,𝔽5)
commutatorC2×C5C2×C4×C25
FrattiniC2×C5C2×C5×AGL(1,𝔽5)
FittingC4×C5×C25C4
socleC2×C52C2×C4×C5
prime radical, cosocleC2×C5×D5C22×C5
hypercenterC4×C25AGL(1,𝔽5)
hypocenterC5C4⋊C4×C25
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C25 ◁ C4×C25

84 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, 279);