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C22×#65700 #13043859

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×#65700
unambiguous semidirect productD5⋊(C2×#388)

Splittings

FittingC22×C5×C22⋊C4 ⋊ C4
SylowC5 ⋊ C22×#388

Subgroups

subgroupG/H
centerC24C22×AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC22×C5×C22⋊C4C4
socleC24×C5C22×C4
prime radicalC25×D5C22
cosocleC22×D5C25
hypercenterC22×C22⋊C4AGL(1,𝔽5)
hypocenterC5C22×#388
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C22⋊C4

5966 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, 1114127);