Finite Group Databasebeta

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C4×#170⋊C8 #13015240

order1280
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C43

Aliases

direct productC4×#170⋊C8

Splittings

SylowC5 ⋊ C4×#322

Subgroups

subgroupG/H
centerC2×C42C2×AGL(1,𝔽5)
commutatorC2×C5C42×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×C8C4
socle, prime radicalC23×C5C2×C42
cosocleC2×C4×Dic5C23
hypercenterC2×C4×C8AGL(1,𝔽5)
hypocenterC5C4×#322
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1085508);