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C₂×#61623 #10577224

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

Aliases

Subgroups

7990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,9)(6,8)(7,10)(11,12)(13,18)(14,23)(15,20)(16,25)(17,21)(19,24)(22,26);(3,5)(4,7)(6,10)(8,9)(11,13,17,14)(12,18,21,23)(15,24,16,22)(19,25,26,20);(11,14,17,13)(12,19,21,26)(15,24,16,22)(18,25,23,20);(5,10)(7,9);(4,8)(7,9)(11,15,17,16)(12,20,21,25)(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, 10484420);