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C₂×#37849 #7635167

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

Aliases

Subgroups

6796 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542363);