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C3⋊(C3⋊AGL(1,𝔽9)) #10620190

order648
isoclinismisoclinic class of C3⋊(C3⋊AGL(1,𝔽9))
automorphism?
homologyAbelianization (H1) = C8 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊(C3⋊AGL(1,𝔽9))

Splittings

Fitting, socle, derived, SylowC34 ⋊ C8

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC34C8
prime radicalC32×C3⋊D3C4
cosocleC32×#157C2
LCSG ▷ C34
UCSC1

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Polycyclic presentation:

2^3,3^4|a^2=b,b^2=c,d^a=d^2e^2,e^a=d^2,f^a=f^2,g^a=g^2,d^b=d^2e,e^b=de,d^c=d^2,e^c=e^2

Conjugacy classes & character table

33 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C3⋊AGL(1,𝔽9), C3⋊D3×AGL(1,𝔽9), #13049796, …
maximal normal subgroup ofD3×C3⋊AGL(1,𝔽9), C3⋊D3×AGL(1,𝔽9), #13049796, …
maximal quotient ofC3⋊(C3⋊#3771), C2×C3⋊(C3⋊AGL(1,𝔽9)), C3⋊(C9⋊AGL(1,𝔽9)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 709);