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C₂×#37249 #7634517

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

Aliases

Subgroups

7402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7541713);