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C2×#10598581 #13023733

order1280
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×#10598581

Splittings

SylowC5 ⋊ C2×Q8⋊C16

Subgroups

subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC4×C5C22×C16
FrattiniC42C22×AGL(1,𝔽5)
FittingC2×C5×C4⋊C8C4
socle, prime radicalC23×C5C22⋊C8
cosocleC4×#168C23
hypercenterC2×C4⋊C8AGL(1,𝔽5)
hypocenterC5C2×Q8⋊C16
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊C8

382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1094001);