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C2×D5⋊#364 #13043389

order1280
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×D5⋊#364
unambiguous semidirect productD5⋊(C2×#364)

Splittings

SylowC5 ⋊ C22×#364

Subgroups

subgroupG/H
centerC2×C8C4⋊AGL(1,𝔽5)
commutatorC4×C5C23×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C4×C5×C8C4
socleC22×C5C2×C4⋊C8
prime radicalC23×D5M16
cosocleC2×#168C24
hypercenterC2×C4×C8AGL(1,𝔽5)
hypocenterC5C22×#364
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×C4×C8

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1113657);