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C₂×#62093 #10578889

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

Aliases

Subgroups

6882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10486085);