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C2×#10604114 #13043126

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#10604114

Splittings

FittingC2×C5×M32 ⋊ C4
SylowC5 ⋊ C22×#347

Subgroups

subgroupG/H
centerC2×C4C2×C4×AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC8C23×AGL(1,𝔽5)
FittingC2×C5×M32C4
socleC22×C5C2×#97
prime radicalC23×D5M16
cosocleC8×D5C24
hypercenterC2×M32AGL(1,𝔽5)
hypocenterC5C22×#347
LCSG ▷ C4×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×M32

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×#347, C2×#13026054, C2×D5⋊AGL(1,ℤ/16), …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#347, C2×#13026054, C2×D5⋊AGL(1,ℤ/16), …
maximal quotient ofC2×#72242137

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1113394);