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Q16×D5⋊C8 #13031563

order1280
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productQ16×D5⋊C8
unambiguous semidirect productD5⋊(C8×Q16)

Splittings

SylowC5 ⋊ C2×C8×Q16

Subgroups

subgroupG/H
centerC2×C4D4×AGL(1,𝔽5)
commutatorC4×C5C23×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC4×C5×Q16C4
socleC22×C5C2×C4×D4
prime radicalC22×D5C4×D4
cosocleC4×Dic5C24
hypercenterC4×Q16AGL(1,𝔽5)
hypocenterC5C2×C8×Q16
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1101831);