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C22×#65761 #13044461

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#65761

Splittings

SylowC5 ⋊ C22×#413

Subgroups

subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC24×C4×C5C4
socleC23×C5C2×C22⋊C4
prime radicalC23×#709C2
cosocleC2×Dic5C25
hypercenterC24×C4AGL(1,𝔽5)
hypocenterC5C22×#413
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

5118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114729);