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C₂×#62045 #10578839

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

Aliases

Subgroups

6850 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)(13,18)(14,23)(15,21)(16,25)(17,20)(19,24)(22,26);(3,4)(5,8)(6,7)(9,10)(11,13,17,14)(12,18,20,23)(15,24,16,22)(19,25,26,21);(11,14,17,13)(12,19,20,26)(15,24,16,22)(18,25,23,21);(4,7)(8,10)(12,20)(18,23)(19,26)(21,25);(3,5,6,9)(4,8,7,10)(11,15,17,16)(12,21,20,25)(13,22,14,24)(18,26,23,19)

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10486035);