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C₂×#59923 #7666768

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

Aliases

Subgroups

6218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573964);