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C2×C4×D4×AGL(1,𝔽5) #13043830

order1280
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×C4×D4×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C42×D4)

Splittings

FittingC2×C4×C5×D4 ⋊ C4
SylowC5 ⋊ C2×C42×D4

Subgroups

subgroupG/H
centerC22×C4C22×AGL(1,𝔽5)
commutatorC2×C5C23×C42
FrattiniC22C24×AGL(1,𝔽5)
FittingC2×C4×C5×D4C4
socleC23×C5C23×C4
prime radicalC22×D4×D5C22
cosocleC22×D5C25
hypercenterC2×C4×D4AGL(1,𝔽5)
hypocenterC5C2×C42×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

5694 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×D42×AGL(1,𝔽5), C2×C4×#11717363, C2×AGL(1,𝔽5)×#442, …
maximal normal subgroup ofC2×D42×AGL(1,𝔽5), C2×AGL(1,𝔽5)×#442, C2×AGL(1,𝔽5)×#532, …
maximal quotient ofAGL(1,𝔽5)×#2956, C2×C4×#11717363, C2×AGL(1,𝔽5)×#442, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114098);