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C2×D5⋊(Q8⋊C8) #13029664

order1280
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D5⋊(Q8⋊C8)
unambiguous semidirect productD5⋊(C2×Q8⋊C8)

Splittings

SylowC5 ⋊ C22×Q8⋊C8

Subgroups

subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC4×C5C23×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C4×C5×Q8C4
socleC23×C5C2×C22⋊C4
prime radicalC23×D5C22⋊C4
cosocleC4×Dic5C24
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5C22×Q8⋊C8
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

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, 1099932);