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C₂×#62057 #10578852

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

Aliases

Subgroups

7056 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10486048);