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C4×AGL(1,𝔽5)×C25 #14522315

order2000
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C42×C25 · Schur multiplier (H2) = C4

Aliases

direct productC4×AGL(1,𝔽5)×C25

Splittings

FittingC4×C5×C25 ⋊ C4
derivedC5 ⋊ C42×C25
SylowC5×C25 ⋊ C42

Subgroups

subgroupG/H
center, hypercenterC4×C25AGL(1,𝔽5)
commutator, hypocenterC5C42×C25
FrattiniC2×C5C2×C5×AGL(1,𝔽5)
FittingC4×C5×C25C4
socleC2×C52C2×C4×C5
prime radical, cosocleC2×C5×D5C22×C5
LCSG ▷ C5
UCSC1 ◁ C4×C25

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 400

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 278);