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C₂×#62793 #10585971

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

Aliases

Subgroups

34874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493167);