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C₂×#59220 #7666966

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

Aliases

Subgroups

7022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7574162);