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C5×#41×AGL(1,𝔽5) #13107732

order1600
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#41×AGL(1,𝔽5)

Splittings

FittingC52×#41 ⋊ C4
SylowC52 ⋊ C4×#41

Subgroups

subgroupG/H
centerC4×C5C22×AGL(1,𝔽5)
commutatorC2×C5C23×C4×C5
FrattiniC2C23×C5×AGL(1,𝔽5)
FittingC52×#41C4
socleC2×C52C23×C4
prime radicalC5×D5×#41C2
cosocleC2×D5C24×C5
hypercenterC5×#41AGL(1,𝔽5)
hypocenterC5C4×C5×#41
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C5 ◁ C5×#41

640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×AGL(1,𝔽5)×H(5,𝔽2), C5×AGL(1,𝔽5)×AGL(1,ℤ/8), C5×AGL(1,𝔽5)×#104, …
maximal normal subgroup ofC5×AGL(1,𝔽5)×H(5,𝔽2), C5×AGL(1,𝔽5)×AGL(1,ℤ/8), C5×AGL(1,𝔽5)×#104
maximal quotient of#41×AGL(1,ℤ/25)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 10084);