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C₂×#59214 #7666338

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

Aliases

Subgroups

6190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573534);