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M16×C3⋊AGL(1,ℤ/9) #72254607

order2592
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C3

Aliases

direct productM16×C3⋊AGL(1,ℤ/9)

Splittings

FittingC3×M16×3−1+2 ⋊ C2
SylowC3×3−1+2 ⋊ C2×M16

Subgroups

subgroupG/H
centerC4C22×C3⋊AGL(1,ℤ/9)
commutatorC2×C3×C9C22×C3×C4
FrattiniC3×C4C22×C3×C3⋊D3
FittingC3×M16×3−1+2C2
socleC2×C32C2×C3×C4×D3
prime radicalC22×C3⋊AGL(1,ℤ/9)C4
cosocleC3×C4×C9C23×C3
hypercenterM16C3⋊AGL(1,ℤ/9)
hypocenterC3×C9C2×C3×M16
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C4 ◁ M16

770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofM16×#92314, AGL(1,ℤ/8)×C3⋊AGL(1,ℤ/9)
maximal normal subgroup ofAGL(1,ℤ/8)×C3⋊AGL(1,ℤ/9)
maximal quotient of#97×C3⋊AGL(1,ℤ/9), M16×#92314

GAP

Past the SmallGroups library coverage — no SmallGroups id.