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C22×#64896 #13033175

order1280
isoclinismisoclinic class of #3993
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC22×#64896

Splittings

SylowC5 ⋊ C22×#341

Subgroups

subgroupG/H
centerC24C4⋊AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC23×C5×C8C4
socleC24×C5C4⋊C4
prime radicalC24×D5Q8
cosocleC2×C4×D5C24
hypercenterC23×C8AGL(1,𝔽5)
hypocenterC5C22×#341
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

2238 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

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, 1103443);