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C2×D5⋊#350 #13043174

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

Aliases

direct productC2×D5⋊#350
unambiguous semidirect productD5⋊(C2×#350)

Splittings

SylowC5 ⋊ C22×#350

Subgroups

subgroupG/H
centerC2×C8C22⋊AGL(1,𝔽5)
commutatorC4×C5C23×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×#131C4
socleC22×C5C2×C22⋊C8
prime radicalC2×D5×#41C4
cosocleC2×#168C24
hypercenterC2×#131AGL(1,𝔽5)
hypocenterC5C22×#350
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#131

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

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, 1113442);