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AGL(1,ℤ/9)×AGL(1,ℤ/16) #72244385

order6912
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/9)×AGL(1,ℤ/16)

Splittings

Fitting3−1+2×AGL(1,ℤ/16) ⋊ C2
Sylow3−1+2 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC2AGL(1,ℤ/9)×#442
commutatorC8×C9C23×C3×C4
FrattiniC2×C3×C8C23×C3×D3
Fitting3−1+2×AGL(1,ℤ/16)C2
socleC2×C3C3×D3×#442
prime radicalAGL(1,ℤ/9)×#509C2
cosocleC2×C8×C9C24×C3
hypercenterAGL(1,ℤ/16)AGL(1,ℤ/9)
hypocenterC9C2×C3×AGL(1,ℤ/16)
LCSG ▷ C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

2207 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

holomorph ofC9×C16

GAP

Past the SmallGroups library coverage — no SmallGroups id.