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C₂×#37194 #7634574

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

5650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7541770);