Finite Group Databasebeta

← Prev (#72220162) Next (#72220164) →

M16×AΓL(1,𝔽9) #72220163

order2304
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×AΓL(1,𝔽9)

Splittings

FittingC32×M16 ⋊ SD16
SylowC32 ⋊ M16×SD16

Subgroups

subgroupG/H
center, FrattiniC4C22×AΓL(1,𝔽9)
commutatorC2×#157C23×C4
FittingC32×M16SD16
socleC2×C32C2×C4×SD16
prime radicalC22×GO+(4,𝔽2)C2×C4
cosocleC4×#157C24
hypercenterM16AΓL(1,𝔽9)
hypocenterC32M16×SD16
LCSG ▷ C2×#157 ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C4 ◁ M16

865 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofM16×AGL(2,𝔽3), AGL(1,ℤ/8)×AΓL(1,𝔽9)
maximal normal subgroup ofAGL(1,ℤ/8)×AΓL(1,𝔽9)
maximal quotient of#97×AΓL(1,𝔽9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.