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C₂×#51943 #7707935

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

Aliases

Subgroups

6780 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7615131);