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C3⋊(3−1+2⋊C8) #10619723

order648
isoclinismisoclinic class of C3⋊AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C3×C8 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊(3−1+2⋊C8)

Splittings

derivedC3×C9 ⋊ C3×C8
SylowC3×3−1+2 ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC4C3⋊AGL(1,ℤ/9)
commutator, hypocenterC3×C9C3×C8
FrattiniC3×C4C3×C3⋊D3
FittingC3×C4×3−1+2C2
socleC2×C32C3×Dic3
prime radicalC2×C33Dic3
cosocleC3×C4×C9C2×C3
LCSG ▷ C3×C9
UCSC1 ◁ C4

107 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Polycyclic presentation:

2,3,2^2,3^3|a^2=c,c^2=d,e^3=g,e^a=e^2g^2,f^a=f^2,g^a=g^2,e^b=eg

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3⋊C8×AGL(1,ℤ/9), #88413⋊C3, D3×3−1+2⋊C8, …
maximal normal subgroup ofC3⋊C8×AGL(1,ℤ/9), #88413⋊C3, D3×3−1+2⋊C8, …
maximal quotient ofC3⋊(3−1+2⋊C16), C2×C3⋊(3−1+2⋊C8), C3⋊#10619495, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 242);