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C₂×#61274 #10576620

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

Aliases

Subgroups

6652 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483816);