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C₂×#36607 #7630322

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

Aliases

Subgroups

9092 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537518);