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C2×#10598563 #13016375

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

Aliases

direct productC2×#10598563

Splittings

SylowC5 ⋊ C2×#1301

Subgroups

subgroupG/H
centerC23(C2×AGL(1,𝔽5))⋊C4
commutatorC2×C4×C5C2×C42
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C22⋊C8C4
socleC23×C5#95
prime radicalC24×C5C4⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C22⋊C8AGL(1,𝔽5)
hypocenterC5C2×#1301
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊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, 1086643);