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C2×D5⋊(C4⋊C16) #13043370

order1280
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC2×D5⋊(C4⋊C16)
unambiguous semidirect productD5⋊(C2×C4⋊C16)

Splittings

SylowC5 ⋊ C22×C4⋊C16

Subgroups

subgroupG/H
centerC22×C8C2×AGL(1,𝔽5)
commutatorC2×C5C23×C16
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C4×C5×C8C4
socleC23×C5C22×C8
prime radicalC23×D5C2×C8
cosocleC2×#168C24
hypercenterC2×C4×C8AGL(1,𝔽5)
hypocenterC5C22×C4⋊C16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

862 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, 1113638);