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C₂×#61475 #10576811

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

Aliases

Subgroups

6900 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10484007);