Finite Group Databasebeta

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C4×#65788 #13033838

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#65788

Splittings

SylowC5 ⋊ C4×#446

Subgroups

subgroupG/H
centerC22×C4C22×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FrattiniC23C23×AGL(1,𝔽5)
FittingC2×C4×C5×Q8C4
socle, prime radicalC23×C5C23×C4
cosocleC22×Dic5C24
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5C4×#446
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

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, 1104106);