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C2×AGL(1,𝔽5)×C25 #11758709

order1000
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C4×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×AGL(1,𝔽5)×C25
unambiguous semidirect productD5⋊(C4×C25)

Splittings

FittingC2×C5×C25 ⋊ C4
derivedC5 ⋊ C2×C4×C25
SylowC5×C25 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC2×C25AGL(1,𝔽5)
commutator, hypocenterC5C2×C4×C25
FrattiniC5C2×C5×AGL(1,𝔽5)
FittingC2×C5×C25C4
socleC2×C52C4×C5
prime radicalC2×C5×D5C2×C5
cosocleC5×D5C22×C5
LCSG ▷ C5
UCSC1 ◁ C2×C25

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 200

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×Dic25, #14522277, (C2×AGL(1,𝔽5))⋊D25, …
maximal normal subgroup ofAGL(1,𝔽5)×Dic25, #14522277, (C2×AGL(1,𝔽5))⋊D25, …
maximal quotient ofC25×D5⋊C8, C25×#700, C4×AGL(1,𝔽5)×C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1000, 94);