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C2×#10617448 #13044764

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

Aliases

direct productC2×#10617448

Splittings

FittingC2×C5×AGL(1,ℤ/8) ⋊ C4
SylowC5 ⋊ C2×#2955

Subgroups

subgroupG/H
centerC22C2×D4×AGL(1,𝔽5)
commutatorC4×C5C24×C4
FrattiniC4C24×AGL(1,𝔽5)
FittingC2×C5×AGL(1,ℤ/8)C4
socleC22×C5C2×C4×D4
prime radicalC2×#66107C2
cosocleC4×D5C25
hypercenterC2×AGL(1,ℤ/8)AGL(1,𝔽5)
hypocenterC5C2×#2955
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

2666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1115032);