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D8×#700 #13032697

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

Aliases

direct productD8×#700

Splittings

SylowC5 ⋊ M16×D8

Subgroups

subgroupG/H
centerC22C2×D4×AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC4×C5×D8C4
socleC22×C5C2×C4×D4
prime radicalC2×D5×D8C4
cosocleC4×Dic5C24
hypercenterC4×D8AGL(1,𝔽5)
hypocenterC5M16×D8
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1102965);