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C2×#10598596 #13016373

order1280
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#10598596

Splittings

SylowC5 ⋊ C2×#1301

Subgroups

subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C2×C42
FrattiniC42C22×AGL(1,𝔽5)
FittingC2×C5×C4⋊C8C4
socleC23×C5#95
prime radicalC23×D5C4⋊C4
cosocleC42×D5C23
hypercenterC2×C4⋊C8AGL(1,𝔽5)
hypocenterC5C2×#1301
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊C8

666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1086641);