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C₂×#39634 #7637284

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

Aliases

Subgroups

6362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7544480);