Finite Group Databasebeta

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C4×#65693 #13033732

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#65693

Splittings

SylowC5 ⋊ C4×#435

Subgroups

subgroupG/H
centerC22×C4C22×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FrattiniC23C23×AGL(1,𝔽5)
FittingC4×C5×C22⋊C4C4
socleC23×C5C23×C4
prime radicalC22×C22⋊D5C2×C4
cosocleC22×Dic5C24
hypercenterC4×C22⋊C4AGL(1,𝔽5)
hypocenterC5C4×#435
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

1282 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

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, 1104000);