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AGL(1,𝔽5)×#350 #13025694

order1280
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productAGL(1,𝔽5)×#350

Splittings

FittingC5×#350 ⋊ C4
SylowC5 ⋊ C4×#350

Subgroups

subgroupG/H
centerC8D4×AGL(1,𝔽5)
commutatorC4×C5C2×C4×C8
FrattiniC2×C8C22×AGL(1,𝔽5)
FittingC5×#350C4
socleC2×C5C4×C22⋊C8
prime radicalD5×#41C2×C4
cosocleC2×C8×D5C23
hypercenter#350AGL(1,𝔽5)
hypocenterC5C4×#350
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C8 ◁ C2×C8 ◁ #350

490 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)×#2171
maximal normal subgroup ofAGL(1,𝔽5)×#2171

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1095962);