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C₂×#51135 #7707124

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

Aliases

Subgroups

6218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7614320);