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AGL(1,𝔽5)×#475 #13036596

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productAGL(1,𝔽5)×#475

Splittings

FittingC5×#475 ⋊ C4
SylowC5 ⋊ C4×#475

Subgroups

subgroupG/H
centerC22C2×D4×AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#475C4
socleC22×C5C2×C4×D4
prime radicalC22×D5C22×D4
cosocleC2×C4×D5C24
hypercenter#475AGL(1,𝔽5)
hypocenterC5C4×#475
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #475

880 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

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, 1106864);