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C₂×#50661 #7706358

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

Aliases

Subgroups

7680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7613554);