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AGL(1,𝔽5)×#563 #13044197

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productAGL(1,𝔽5)×#563

Splittings

FittingC5×#563 ⋊ C4
SylowC5 ⋊ C4×#563

Subgroups

subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#563C4
prime radicalC2×D4×D5C23
cosocleC22×D5C25
hypercenter#563AGL(1,𝔽5)
hypocenterC5C4×#563
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #563

2024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

95 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114465);