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#6875⋊C4 #11757309

order972
isoclinismisoclinic class of AGL(1,ℤ/27)
automorphism?
homologyAbelianization (H1) = C4×C9 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#6875⋊C4

Splittings

derivedC27 ⋊ C4×C9
Sylow#6875 ⋊ C4

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,ℤ/27)
commutator, hypocenterC27C4×C9
FrattiniC2×C3×C9C3×D3
FittingC2×#6875C2
socleC2×C3D9⋊C9
prime radicalC2×C32AGL(1,ℤ/9)
cosocleC2×C27⋊C3C2×C3
LCSG ▷ C27
UCSC1 ◁ C2

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Polycyclic presentation:

2,3,2,3^4|a^2=c,b^3=d,e^3=f,f^3=g,e^a=e^2f^2g^2,f^a=f^2g^2,g^a=g^2,e^b=ef^2g^2,f^b=fg^2,e^d=eg^2

Conjugacy classes & character table

62 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#6875⋊Q8, C4×AGL(1,ℤ/27), C2×#6875⋊C4, …
maximal normal subgroup of#6875⋊Q8, C4×AGL(1,ℤ/27), C2×#6875⋊C4, …
maximal quotient of#6875⋊C8, C2×#6875⋊C4, #72229362, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 34);