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C3×3−1+2⋊AGL(1,𝔽5) #13108367

order1620
isoclinismisoclinic class of 3−1+2⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×3−1+2⋊AGL(1,𝔽5)
unambiguous semidirect product(C9⋊AGL(1,𝔽5))⋊C32
unambiguous semidirect product(C3×C9⋊AGL(1,𝔽5))⋊C3

Splittings

Fitting, HallC3×C5×3−1+2 ⋊ C4
derivedC5×C9 ⋊ C32×C4
SylowC3×3−1+2 ⋊ AGL(1,𝔽5)
SylowC5 ⋊ C3×3−1+2⋊C4

Subgroups

subgroupG/H
center, hypercenterC33−1+2⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C32×C4
FrattiniC3C32×ΓL(1,𝔽16)
FittingC3×C5×3−1+2C4
socleC32×C5C3×Dic3
prime radicalC33×D5D3
cosocleC9×D5C2×C32
LCSG ▷ C5×C9
UCSC1 ◁ C3

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 90

Conjugacy classes & character table

93 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72222360, C3×AGL(1,𝔽5)×AGL(1,ℤ/9), D3×3−1+2⋊AGL(1,𝔽5), …
maximal normal subgroup of#72222360, C3×AGL(1,𝔽5)×AGL(1,ℤ/9), D3×3−1+2⋊AGL(1,𝔽5), …
maximal quotient of#72222360, #72247426, A4×3−1+2⋊AGL(1,𝔽5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 273);