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C₂×#37134 #7634429

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

Aliases

Subgroups

7186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541625);