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C₂×#40688 #7638659

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

Aliases

Subgroups

7224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4)(5,9)(6,7)(8,10)(11,12)(13,18)(14,17)(15,16);(4,7)(8,9)(12,16)(14,18)(19,20)(21,25)(22,23)(24,26);(5,10)(8,9)(12,16)(13,17)(20,23)(24,25);(3,5)(4,8)(6,10)(7,9)(11,13,15,17)(12,14,16,18)(19,20)(21,24)(22,23)(25,26);(3,4)(5,8)(6,7)(9,10)(11,14)(12,17)(13,16)(15,18)(19,21)(20,24)(22,26)(23,25)

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, 7545855);