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C2×D5⋊#349 #13043163

order1280
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D5⋊#349
unambiguous semidirect productD5⋊(C2×#349)

Splittings

SylowC5 ⋊ C22×#349

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C23×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC22×C5×M16C4
socleC22×C5C2×C22⋊C8
prime radicalC24×D5C8
cosocleC2×#168C24
hypercenterC22×M16AGL(1,𝔽5)
hypocenterC5C22×#349
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22×M16

1262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1113431);