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C2×AGL(1,𝔽5)×#121 #13043871

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

Aliases

direct productC2×AGL(1,𝔽5)×#121
unambiguous semidirect productD5⋊(C4×#121)

Splittings

FittingC2×C5×#121 ⋊ C4
SylowC5 ⋊ C2×C4×#121

Subgroups

subgroupG/H
centerC23C23×AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC2×C5×#121C4
socleC23×C5C23×C4
prime radicalC2×D5×#121C2
cosocleC22×D5C25
hypercenterC2×#121AGL(1,𝔽5)
hypocenterC5C2×C4×#121
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#121

5022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D42×AGL(1,𝔽5), C2×AGL(1,𝔽5)×#535, C2×AGL(1,𝔽5)×#532, …
maximal normal subgroup ofC2×D42×AGL(1,𝔽5), C2×AGL(1,𝔽5)×#535, C2×AGL(1,𝔽5)×#532, …
maximal quotient ofAGL(1,𝔽5)×#3068, AGL(1,𝔽5)×#3058, AGL(1,𝔽5)×#3060, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114139);