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C₂×#59269 #7666288

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

Aliases

Subgroups

7022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573484);