Finite Group Databasebeta

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D8×#681 #12070723

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD8×#681

Splittings

SylowC5 ⋊ M16×D8

Subgroups

subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC2×C4×C5×D8C2
socleC22×C5C2×C4×D4
prime radicalC22×C5×D8C4
cosocleC42×C5C24
hypercenterC2×C4×D8D5
hypocenterC5M16×D8
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D8

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 140991);