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C4⋊C4×C3⋊AGL(1,ℤ/9) #72254656

order2592
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC4⋊C4×C3⋊AGL(1,ℤ/9)

Splittings

FittingC3×C4⋊C4×3−1+2 ⋊ C2
SylowC3×3−1+2 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
centerC22C22×C3⋊AGL(1,ℤ/9)
commutatorC2×C3×C9C22×C3×C4
FrattiniC22×C3C22×C3×C3⋊D3
FittingC3×C4⋊C4×3−1+2C2
socleC22×C32C22×C3×D3
prime radicalC22×C3⋊AGL(1,ℤ/9)C22
cosocleC22×C3×C9C23×C3
hypercenterC4⋊C4C3⋊AGL(1,ℤ/9)
hypocenterC3×C9C2×C3×C4⋊C4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

1037 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 432

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#106×C3⋊AGL(1,ℤ/9), C4×D4×C3⋊AGL(1,ℤ/9), #102×C3⋊AGL(1,ℤ/9), …
maximal normal subgroup of#106×C3⋊AGL(1,ℤ/9), C4×D4×C3⋊AGL(1,ℤ/9), #102×C3⋊AGL(1,ℤ/9)
maximal quotient of#106×C3⋊AGL(1,ℤ/9), C4⋊C4×#92314

GAP

Past the SmallGroups library coverage — no SmallGroups id.