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AGL(1,𝔽5)×#381 #13027933

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productAGL(1,𝔽5)×#381

Splittings

FittingC5×#381 ⋊ C4
SylowC5 ⋊ C4×#381

Subgroups

subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FittingC5×#381C4
socleC23×C5C23×C4
prime radicalC24×D5C23
cosocleC23×D5C24
hypercenter#381AGL(1,𝔽5)
hypocenterC5C4×#381
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ #381

2606 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)×#2404, AGL(1,𝔽5)×#2308
maximal normal subgroup ofAGL(1,𝔽5)×#2404, AGL(1,𝔽5)×#2308
maximal quotient ofAGL(1,𝔽5)×#1828

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1098201);