Finite Group Databasebeta

← Prev (#14516661) Next (#14516663) →

C22×AGL(1,ℤ/27) #14516662

order1944
isoclinismisoclinic class of AGL(1,ℤ/27)
automorphism?
homologyAbelianization (H1) = C23×C9 · Schur multiplier (H2) = C23

Aliases

direct productC22×AGL(1,ℤ/27)
unambiguous semidirect product#6875⋊C23
unambiguous semidirect product(C2×#6875)⋊C22

Splittings

FittingC22×#6875 ⋊ C2
derivedC27 ⋊ C23×C9
Sylow#6875 ⋊ C23

Subgroups

subgroupG/H
center, hypercenterC22AGL(1,ℤ/27)
commutator, hypocenterC27C23×C9
FrattiniC3×C9C22×C3×D3
FittingC22×#6875C2
socleC22×C3D9⋊C9
prime radicalC22×D27⋊C3C3
cosocleC27⋊C3C23×C3
LCSG ▷ C27
UCSC1 ◁ C22

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

124 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofA4×AGL(1,ℤ/27), D4×AGL(1,ℤ/27), C2×D3×AGL(1,ℤ/27), …
maximal normal subgroup ofA4×AGL(1,ℤ/27), D4×AGL(1,ℤ/27), C2×C4×AGL(1,ℤ/27), …
maximal quotient ofD4×AGL(1,ℤ/27), C2×D3×AGL(1,ℤ/27), C2×C4×AGL(1,ℤ/27), …
automorphism group ofC27⋊C8, C4×D27, #6171, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 1056);