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C2×#10604806 #13035600

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#10604806
unambiguous semidirect productD5⋊#1978

Splittings

FittingC22×C5×D8 ⋊ C4
SylowC5 ⋊ C2×#1978

Subgroups

subgroupG/H
centerC22#65780
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC22×C5×D8C4
socleC22×C5#390
prime radicalC22×D5×D8C2
cosocleC2×C4×D5C24
hypercenterC22×D8AGL(1,𝔽5)
hypocenterC5C2×#1978
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

1694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1105868);