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AGL(1,𝔽5)×#535 #13043931

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productAGL(1,𝔽5)×#535

Splittings

FittingC5×#535 ⋊ C4
SylowC5 ⋊ C4×#535

Subgroups

subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#535C4
prime radicalD5×#535C2
cosocleC22×D5C25
hypercenter#535AGL(1,𝔽5)
hypocenterC5C4×#535
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #535

3602 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 of#535×#1043, AGL(1,𝔽5)×#3484, AGL(1,𝔽5)×#3498, …
maximal normal subgroup ofAGL(1,𝔽5)×#3484, AGL(1,𝔽5)×#3498, AGL(1,𝔽5)×#3532, …
maximal quotient of#535×#1043, #72221567, #72221687, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114199);