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C2×#10604849 #13035563

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

Aliases

direct productC2×#10604849
unambiguous semidirect productD5⋊#1971

Splittings

FittingC22×C5×Q16 ⋊ C4
SylowC5 ⋊ C2×#1971

Subgroups

subgroupG/H
centerC23D4×AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC22×C5×Q16C4
socleC23×C5C4×D4
prime radicalC23×D5C2×D4
cosocleC2×C4×D5C24
hypercenterC22×Q16AGL(1,𝔽5)
hypocenterC5C2×#1971
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

1574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

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, 1105831);