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C₂×#46338 #7703014

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

Aliases

Subgroups

7690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610210);