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C₂×#36587 #7630298

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

Aliases

Subgroups

6910 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537494);