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C₂×#51695 #7707551

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

Aliases

Subgroups

6304 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7614747);