Finite Group Databasebeta

← Prev (#11757489) Next (#11757491) →

C2×AGL(1,ℤ/27) #11757490

order972
isoclinismisoclinic class of AGL(1,ℤ/27)
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×AGL(1,ℤ/27)
unambiguous semidirect product#6875⋊C22
unambiguous semidirect product(C2×#6875)⋊C2

Splittings

FittingC2×#6875 ⋊ C2
derivedC27 ⋊ C22×C9
Sylow#6875 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,ℤ/27)
commutator, hypocenterC27C22×C9
FrattiniC3×C9C2×C3×D3
FittingC2×#6875C2
socleC2×C3D9⋊C9
prime radicalC2×D27⋊C3C3
cosocleC27⋊C3C22×C3
LCSG ▷ C27
UCSC1 ◁ C2

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 54

Conjugacy classes & character table

62 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×AGL(1,ℤ/27), C4⋊AGL(1,ℤ/27), #14516071, …
maximal normal subgroup ofC4×AGL(1,ℤ/27), C4⋊AGL(1,ℤ/27), #14516071, …
maximal quotient of#6875⋊Q8, C4×AGL(1,ℤ/27), C4⋊AGL(1,ℤ/27), …
automorphism group ofDic27, C2×D27, C3×D27, …
holomorph ofC2×C27

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 215);