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C₂×#51190 #7707112

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

Aliases

Subgroups

6828 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)(12,14)(16,17)(19,20,23,24)(21,25,26,22);(3,5)(4,8)(6,9)(7,10)(11,12,15,14)(13,17,18,16)(20,24)(22,25);(5,10)(8,9)(19,21)(20,22)(23,26)(24,25);(3,5)(4,9)(6,8)(7,10)(11,13,15,18)(12,16,14,17)(19,22)(20,21)(23,25)(24,26);(3,6,7,4)(5,8,10,9)(11,14,15,12)(13,17,18,16)(19,21)(20,22)(23,26)(24,25)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7614308);