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#6899⋊C₂ #92313

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2,3^5|c^3=e^2,d^3=f^2,c^a=c^2e,d^a=d^2f,e^a=e^2,f^a=f^2,c^b=cef,d^b=df

Conjugacy classes & character table

30 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 158);