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AGL(1,𝔽5)×#519 #13043845

order1280
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productAGL(1,𝔽5)×#519

Splittings

FittingC5×#519 ⋊ C4
SylowC5 ⋊ C4×#519

Subgroups

subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutatorC2×C5C23×C42
FittingC5×#519C4
socleC22×C5C24×C4
prime radicalC23×D5C24
cosocleC22×D5C25
hypercenter#519AGL(1,𝔽5)
hypocenterC5C4×#519
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ #519

3402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114113);