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AGL(1,𝔽5)×#518 #13043841

order1280
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productAGL(1,𝔽5)×#518

Splittings

FittingC5×#518 ⋊ C4
SylowC5 ⋊ C4×#518

Subgroups

subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutatorC2×C5C23×C42
FittingC5×#518C4
socleC22×C5C24×C4
prime radicalC22×D4×D5C22
cosocleC22×D5C25
hypercenter#518AGL(1,𝔽5)
hypocenterC5C4×#518
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ #518

4186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#3484, AGL(1,𝔽5)×#1904, #72221755, …
maximal normal subgroup ofAGL(1,𝔽5)×#3484, AGL(1,𝔽5)×#1904, AGL(1,𝔽5)×#1889, …
maximal quotient of#72221755, #518×#1043, AGL(1,𝔽5)×#2308

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114109);