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C₂×#59958 #7665808

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

Aliases

Subgroups

5972 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)(12,16)(17,18)(19,20)(21,24)(22,23)(25,26);(4,7)(8,9)(11,12)(13,17)(14,18)(15,16)(19,21,23,26)(20,24,22,25);(11,13,15,14)(12,17,16,18)(19,21)(20,25)(22,24)(23,26);(3,4)(5,8)(6,7)(9,10)(11,14,15,13)(12,18,16,17)(19,22,23,20)(21,24,26,25);(3,5)(4,8)(6,10)(7,9)(11,12)(13,17)(14,18)(15,16)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573004);