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C₂×#62578 #10579967

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

Aliases

Subgroups

6522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10487163);