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C22×C4⋊#674 #13043369

order1280
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC22×C4⋊#674

Splittings

SylowC5 ⋊ C22×C4⋊C16

Subgroups

subgroupG/H
centerC23×C4C2×AGL(1,𝔽5)
commutatorC2×C5C23×C16
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC22×C42×C5C4
socle, prime radicalC24×C5C2×C8
cosocleC2×#168C24
hypercenterC22×C42AGL(1,𝔽5)
hypocenterC5C22×C4⋊C16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C22×C42

862 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, 1113637);