Finite Group Databasebeta

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C22×#65727 #13044528

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

Aliases

direct productC22×#65727
unambiguous semidirect productD5⋊(C2×#428)

Splittings

FittingC22×C5×M16 ⋊ C4
SylowC5 ⋊ C22×#428

Subgroups

subgroupG/H
centerC23C2×C4⋊AGL(1,𝔽5)
commutatorC4×C5C24×C4
FrattiniC4C24×AGL(1,𝔽5)
FittingC22×C5×M16C4
socleC23×C5C2×C4⋊C4
prime radicalC24×D5D4
cosocleC4×D5C25
hypercenterC22×M16AGL(1,𝔽5)
hypocenterC5C22×#428
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

3182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114796);