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AGL(1,𝔽5)×Dic25 #14522276

order2000
isoclinismisoclinic class of AGL(1,𝔽5)×D25
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C4

Aliases

direct productAGL(1,𝔽5)×Dic25

Splittings

derived, SylowC5×C25 ⋊ C42

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽5)×D25
commutator, hypocenterC5×C25C42
FrattiniC2×C5D5×AGL(1,𝔽5)
FittingC2×C5×C25C2×C4
socleC2×C52C4×D5
prime radicalC2×C5×D5C2×D5
cosocleC2×D5×C25C22
LCSG ▷ C5×C25
UCSC1 ◁ C2

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 400

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 239);