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C₂×#62906 #10586247

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

Aliases

Subgroups

32666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 34 points:

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493443);