Finite Group Databasebeta

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C4×#65680 #13033607

order1280
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#65680

Splittings

SylowC5 ⋊ C4×#431

Subgroups

subgroupG/H
centerC2×C42C2×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C8
FrattiniC23C23×AGL(1,𝔽5)
FittingC43×C5C4
socleC23×C5C23×C4
prime radicalC23×D5C22×C4
cosocleC22×Dic5C24
hypercenterC43AGL(1,𝔽5)
hypocenterC5C4×#431
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C42 ◁ C43

1318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103875);