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#6858⋊C₂ #92200

• supersolvable
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 36 points:

(2,5)(3,8)(4,9)(6,7)(11,14)(12,18)(13,22)(15,17)(16,26)(19,20)(21,32)(23,31)(24,29)(25,27)(28,36)(30,35)(33,34);(1,3,8)(2,6,4)(5,9,7)(10,21,18,13,20,19,22,12,32)(11,28,31,17,33,27,29,16,30)(14,35,26,24,25,34,15,23,36);(1,3,5,9,7,6,4,2,8)(10,29,14,22,17,15,13,11,24)(12,33,35,20,28,23,21,16,25)(18,27,26,32,31,36,19,30,34)

Polycyclic presentation:

2,3^5|b^3=f^2,c^3=e,b^a=b^2f,c^a=c^2e^2,d^a=de^2f,e^a=e^2,f^a=f^2,c^b=cd,d^b=def,d^c=df

Conjugacy classes & character table

22 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 45);