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D42×AGL(1,𝔽5) #13043999

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD42×AGL(1,𝔽5)

Splittings

FittingC5×D42 ⋊ C4
SylowC5 ⋊ C4×D42

Subgroups

subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×D42C4
prime radicalD42×D5C2
cosocleC22×D5C25
hypercenterD42AGL(1,𝔽5)
hypocenterC5C4×D42
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ D42

4804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

125 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#3484, AGL(1,𝔽5)×#3498, AGL(1,𝔽5)×#3532, …
maximal normal subgroup ofAGL(1,𝔽5)×#3484, AGL(1,𝔽5)×#3498, AGL(1,𝔽5)×#3532, …
maximal quotient ofAGL(1,𝔽5)×#3292, AGL(1,𝔽5)×#3291, AGL(1,𝔽5)×#3288, …
automorphism group of#3955, #3956, #4054, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114267);