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C3⋊(#1658⋊C3) #11920175

order1152
isoclinismisoclinic class of C3⋊(#1658⋊C3)
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C22

Aliases

unambiguous semidirect productC3⋊(#1658⋊C3)
unambiguous semidirect product#71960⋊C3

Splittings

Fitting, derivedC3×#564 ⋊ C2×C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×#564C2×C3
FrattiniC42D3×A4
socleC22×C3#120⋊C3
LCSG ▷ C3×#564
UCSC1

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Polycyclic presentation:

2,3,2^4,3,2^2|c^2=h,d^2=hi,e^2=i,f^2=hi,c^a=ce,d^a=defhi,e^a=ei,f^a=fhi,g^a=g^2,c^b=cd,d^b=chi,e^b=fi,f^b=ef,h^b=i,i^b=hi,e^c=ei,f^c=fh,e^d=ehi,f^d=fi

Conjugacy classes & character table

21 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 154186);