Finite Group Databasebeta

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C22×#65721 #13044527

order1280
isoclinismisoclinic class of #3993
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×#65721
unambiguous semidirect productD5⋊(C2×#427)

Splittings

FittingC23×C5×C8 ⋊ C4
SylowC5 ⋊ C22×#427

Subgroups

subgroupG/H
centerC22×C4C4⋊AGL(1,𝔽5)
commutatorC4×C5C24×C4
FrattiniC4C24×AGL(1,𝔽5)
FittingC23×C5×C8C4
socleC23×C5C2×C4⋊C4
prime radicalC24×D5D4
cosocleC4×D5C25
hypercenterC23×C8AGL(1,𝔽5)
hypocenterC5C22×#427
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

3006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

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, 1114795);