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C3×AGL(1,ℤ/27) #13090964

order1458
isoclinismisoclinic class of AGL(1,ℤ/27)
automorphism?
homologyAbelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3

Aliases

direct productC3×AGL(1,ℤ/27)
unambiguous semidirect product(D27⋊C3)⋊C9

Splittings

Fitting, SylowC3×#6875 ⋊ C2
derivedC27 ⋊ C2×C3×C9

Subgroups

subgroupG/H
center, hypercenterC3AGL(1,ℤ/27)
commutator, hypocenterC27C2×C3×C9
FrattiniC3×C9C32×D3
FittingC3×#6875C2
socleC32D9⋊C9
prime radicalC3×D27⋊C3C3
cosocleC27⋊C3C2×C32
LCSG ▷ C27
UCSC1 ◁ C3

113 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 54

Conjugacy classes & character table

93 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×AGL(1,ℤ/27), C2×C3×AGL(1,ℤ/27), #72214322, …
maximal normal subgroup ofC9×AGL(1,ℤ/27), C2×C3×AGL(1,ℤ/27), #72214322, …
maximal quotient ofC9×AGL(1,ℤ/27), C2×C3×AGL(1,ℤ/27), #72214322, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 1038);