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AGL(1,𝔽5)×#435 #13033731

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

Aliases

direct productAGL(1,𝔽5)×#435

Splittings

FittingC5×#435 ⋊ C4
SylowC5 ⋊ C4×#435

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×AGL(1,𝔽5)
commutator, socleC22×C5C22×C42
FittingC5×#435C4
prime radicalC2×D4×D5C2×C4
cosocleC2×C4×D5C24
hypercenter#435AGL(1,𝔽5)
hypocenterC5C4×#435
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #435

1282 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#2970, AGL(1,𝔽5)×#2968
maximal normal subgroup ofAGL(1,𝔽5)×#2970, AGL(1,𝔽5)×#2968

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103999);