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C4×M16×AGL(1,𝔽5) #13033107

order1280
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43

Aliases

direct productC4×M16×AGL(1,𝔽5)

Splittings

FittingC4×C5×M16 ⋊ C4
SylowC5 ⋊ C42×M16

Subgroups

subgroupG/H
centerC42C22×AGL(1,𝔽5)
commutatorC2×C5C2×C43
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC4×C5×M16C4
socleC22×C5C22×C42
prime radicalC23×D5C22×C4
cosocleC2×C4×D5C24
hypercenterC4×M16AGL(1,𝔽5)
hypocenterC5C42×M16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C42 ◁ C4×M16

1734 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 ofC4×M16×#1043, AGL(1,𝔽5)×#3151, AGL(1,𝔽5)×#3184, …
maximal normal subgroup ofAGL(1,𝔽5)×#3151, AGL(1,𝔽5)×#3184, AGL(1,𝔽5)×#1455, …
maximal quotient ofC4×M16×#1043, AGL(1,𝔽5)×#1455, C4×#13103905

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103375);