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C₂×#39684 #7637161

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

Aliases

Subgroups

7014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7544357);