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C42×C5×AGL(1,𝔽5) #13104445

order1600
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C43×C5 · Schur multiplier (H2) = C43

Aliases

direct productC42×C5×AGL(1,𝔽5)

Splittings

FittingC42×C52 ⋊ C4
derivedC5 ⋊ C43×C5
SylowC52 ⋊ C43

Subgroups

subgroupG/H
center, hypercenterC42×C5AGL(1,𝔽5)
commutator, hypocenterC5C43×C5
FrattiniC22C22×C5×AGL(1,𝔽5)
FittingC42×C52C4
socleC22×C52C22×C4
prime radicalC22×C5×D5C23
cosocleC22×D5C23×C5
LCSG ▷ C5
UCSC1 ◁ C42×C5

531 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×AGL(1,𝔽5)×#127, C42×AGL(1,ℤ/25), C5×AGL(1,𝔽5)×#104
maximal normal subgroup ofC5×AGL(1,𝔽5)×#127, C5×AGL(1,𝔽5)×#104
maximal quotient ofC42×AGL(1,ℤ/25)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 6797);