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AGL(1,𝔽5)×AGL(1,ℤ/16) #72220664

order2560
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productAGL(1,𝔽5)×AGL(1,ℤ/16)

Splittings

FittingC5×AGL(1,ℤ/16) ⋊ C4
SylowC5 ⋊ C4×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC2AGL(1,𝔽5)×#442
commutatorC5×C8C22×C42
FrattiniC2×C8C23×AGL(1,𝔽5)
FittingC5×AGL(1,ℤ/16)C4
socleC2×C5C4×#442
prime radicalD5×#509C22
cosocleC2×C8×D5C24
hypercenterAGL(1,ℤ/16)AGL(1,𝔽5)
hypocenterC5C4×AGL(1,ℤ/16)
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

1554 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

115 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72220816, C2×AGL(1,𝔽5)×AGL(1,ℤ/16), #1043×AGL(1,ℤ/16), …
maximal normal subgroup ofC2×AGL(1,𝔽5)×AGL(1,ℤ/16), AGL(1,𝔽5)×#33688
maximal quotient of#72220816, AGL(1,𝔽5)×#12067, C2×AGL(1,𝔽5)×AGL(1,ℤ/16), …
automorphism group ofD80, Dic40
holomorph ofC5×C16

GAP

Past the SmallGroups library coverage — no SmallGroups id.