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AGL(1,𝔽5)×#410 #13033347

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

Aliases

direct productAGL(1,𝔽5)×#410

Splittings

FittingC5×#410 ⋊ C4
SylowC5 ⋊ C4×#410

Subgroups

subgroupG/H
centerC4C22⋊C4×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FrattiniC23C23×AGL(1,𝔽5)
FittingC5×#410C4
socleC2×C5C2×C4×C22⋊C4
prime radicalC2×D5×#41C22
cosocleC23×D5C24
hypercenter#410AGL(1,𝔽5)
hypocenterC5C4×#410
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

1666 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)×#1904, AGL(1,𝔽5)×#2008, AGL(1,𝔽5)×#1910, …
maximal normal subgroup ofAGL(1,𝔽5)×#1904, AGL(1,𝔽5)×#2008, AGL(1,𝔽5)×#1910, …
maximal quotient of#72221657, #72226525, #72226553

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103615);