Finite Group Databasebeta

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C4×#65711 #13027923

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#65711

Splittings

FittingC4×C5×C4⋊C4 ⋊ C4
SylowC5 ⋊ C4×#387

Subgroups

subgroupG/H
centerC22×C4C22×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FrattiniC23C23×AGL(1,𝔽5)
FittingC4×C5×C4⋊C4C4
socleC23×C5C23×C4
prime radical, cosocleC23×D5C24
hypercenterC4×C4⋊C4AGL(1,𝔽5)
hypocenterC5C4×#387
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

1742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1098191);