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C22×#65731 #13044733

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

Aliases

direct productC22×#65731
unambiguous semidirect productD5⋊(C2×#442)

Splittings

FittingC22×C5×D8 ⋊ C4
SylowC5 ⋊ C22×#442

Subgroups

subgroupG/H
centerC23D4×AGL(1,𝔽5)
commutatorC4×C5C24×C4
FrattiniC4C24×AGL(1,𝔽5)
FittingC22×C5×D8C4
socleC23×C5C4×D4
prime radicalC22×D5×D8C2
cosocleC4×D5C25
hypercenterC22×D8AGL(1,𝔽5)
hypocenterC5C22×#442
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

3654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×#442, C2×D5⋊AGL(1,ℤ/16), C2×#13025913, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#442, C2×D5⋊AGL(1,ℤ/16), C2×#13025913
maximal quotient ofC2×D5⋊AGL(1,ℤ/16), C22×#13104743

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1115001);