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C3⋊#10617014 #14513675

order1920
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊#10617014

Splittings

FittingC3×#564 ⋊ D5
derivedC3×#564⋊C5 ⋊ C2
SylowC3 ⋊ #10617014

Subgroups

subgroupG/H
center, Frattini, hypercenterC22C3⋊((C24⋊C5)⋊C2)
commutator, cosocle, hypocenterC3×#564⋊C5C2
FittingC3×#564D5
socleC22×C3(C24⋊C5)⋊C2
LCSG ▷ C3×#564⋊C5
UCSC1 ◁ C22

154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Polycyclic presentation:

2,3,5,2^6|d^2=h,e^2=h,f^2=hi,g^2=i,b^a=b^2,c^a=c^4,d^a=defgh,e^a=egi,f^a=fghi,g^a=gi,d^c=e,e^c=ef,f^c=fg,g^c=dgh,e^d=ehi,f^d=fh,g^d=gh,f^e=fhi,g^e=gi,g^f=gi

Conjugacy classes & character table

45 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 239373);