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C2×#10604033 #13033501

order1280
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#10604033

Splittings

FittingC2×C5×C4⋊C8 ⋊ C4
SylowC5 ⋊ C2×C8×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C22×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×C4⋊C8C4
socleC23×C5C2×C42
prime radicalC23×D5C22×C4
cosocleC2×C4×D5C24
hypercenterC2×C4⋊C8AGL(1,𝔽5)
hypocenterC5C2×C8×C4⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103769);