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C4×#64881 #13017290

order1280
isoclinismisoclinic class of #3993
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#64881

Splittings

SylowC5 ⋊ C4×#334

Subgroups

subgroupG/H
centerC22×C4C4⋊AGL(1,𝔽5)
commutatorC4×C5C2×C4×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×C8C4
socle, prime radicalC23×C5C2×C4⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4×C8AGL(1,𝔽5)
hypocenterC5C4×#334
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1087558);