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C₂×#36203 #7629842

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

Aliases

Subgroups

7530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537038);