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C2×D5⋊#410 #13044445

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×D5⋊#410
unambiguous semidirect productD5⋊(C2×#410)

Splittings

FittingC22×C5×#41 ⋊ C4
SylowC5 ⋊ C22×#410

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC22×C5×#41C4
socleC22×C5C22×C22⋊C4
prime radicalC22×D5×#41C2
cosocleC22×D5C25
hypercenterC22×#41AGL(1,𝔽5)
hypocenterC5C22×#410
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

5278 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, 1114713);