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AGL(1,𝔽5)×#444 #13033811

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productAGL(1,𝔽5)×#444

Splittings

FittingC5×#444 ⋊ C4
SylowC5 ⋊ C4×#444

Subgroups

subgroupG/H
centerC4C2×D4×AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#444C4
socleC2×C5C42×D4
prime radicalD5×#135C22
cosocleC2×C4×D5C24
hypercenter#444AGL(1,𝔽5)
hypocenterC5C4×#444
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C2×C8 ◁ #444

1022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×AGL(1,ℤ/16), #72220809, AGL(1,𝔽5)×#3288, …
maximal normal subgroup ofAGL(1,𝔽5)×AGL(1,ℤ/16), AGL(1,𝔽5)×#3288, AGL(1,𝔽5)×#2956, …
maximal quotient of#72220809, #72223429, AGL(1,𝔽5)×#1580, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1104079);