Finite Group Databasebeta

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C22×#65712 #13043861

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

Aliases

direct productC22×#65712
unambiguous semidirect productD5⋊(C2×#389)

Splittings

FittingC22×C5×C4⋊C4 ⋊ C4
SylowC5 ⋊ C22×#389

Subgroups

subgroupG/H
centerC24C22×AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC24×C5C22×C4
prime radicalC24×D5C23
cosocleC22×D5C25
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5C22×#389
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C4⋊C4

4894 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, 1114129);