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C₃⋊#564 #5686

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 35 points:

(1,2,3)(5,11)(9,17)(10,19)(16,18)(20,23,24,31)(21,27,26,34)(22,29,28,30)(25,32,33,35);(4,7,8,15)(5,10,11,19)(6,12,13,14)(9,16,17,18)(21,26)(22,28)(27,34)(29,30);(4,6,8,13)(5,9,11,17)(7,14,15,12)(10,18,19,16)(20,22)(21,25)(23,30)(24,28)(26,33)(27,35)(29,31)(32,34);(2,3)(4,5)(6,9)(7,10)(8,11)(12,16)(13,17)(14,18)(15,19)(20,21,24,26)(22,25,28,33)(23,27,31,34)(29,32,30,35)

Polycyclic presentation:

2^6,3|a^2=f,b^2=e,c^2=e,d^2=f,c^a=cf,d^a=de,g^a=g^2,c^b=cef,d^b=df

Conjugacy classes & character table

33 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1245);