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C₂×#37150 #7634447

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

Aliases

Subgroups

6406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541643);