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C2×AGL(1,𝔽5)×M32 #13043097

order1280
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×AGL(1,𝔽5)×M32

Splittings

FittingC2×C5×M32 ⋊ C4
SylowC5 ⋊ C2×C4×M32

Subgroups

subgroupG/H
centerC2×C8C22×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C8
FrattiniC8C23×AGL(1,𝔽5)
FittingC2×C5×M32C4
socleC22×C5C2×C4×C8
prime radicalC23×D5C2×C8
cosocleC8×D5C24
hypercenterC2×M32AGL(1,𝔽5)
hypocenterC5C2×C4×M32
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ C2×M32

918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×#347, C2×AGL(1,𝔽5)×#365, C2×AGL(1,𝔽5)×#509, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#347, C2×AGL(1,𝔽5)×#365, C2×AGL(1,𝔽5)×#509, …
maximal quotient ofC2×M32×#1043

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1113365);