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AGL(1,𝔽5)×#486 #13036686

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productAGL(1,𝔽5)×#486

Splittings

FittingC5×#486 ⋊ C4
SylowC5 ⋊ C4×#486

Subgroups

subgroupG/H
centerC22C2×D4×AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#486C4
socleC22×C5C2×C4×D4
prime radicalD5×#127C22
cosocleC2×C4×D5C24
hypercenter#486AGL(1,𝔽5)
hypocenterC5C4×#486
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #486

1046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#1721, AGL(1,𝔽5)×#3184, AGL(1,𝔽5)×#1715, …
maximal normal subgroup ofAGL(1,𝔽5)×#1721, AGL(1,𝔽5)×#3184, AGL(1,𝔽5)×#1715
maximal quotient of#486×#1043

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1106954);