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C2×AGL(1,𝔽5)×#123 #13043872

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

Aliases

direct productC2×AGL(1,𝔽5)×#123
unambiguous semidirect productD5⋊(C4×#123)

Splittings

FittingC2×C5×#123 ⋊ C4
SylowC5 ⋊ C2×C4×#123

Subgroups

subgroupG/H
centerC23C23×AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC2×C5×#123C4
socleC23×C5C23×C4
prime radicalC22×D4×D5C22
cosocleC22×D5C25
hypercenterC2×#123AGL(1,𝔽5)
hypocenterC5C2×C4×#123
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#123

4070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114140);