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C₂×#43492 #7667675

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

Aliases

Subgroups

12282 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574871);