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C₂×#37911 #7635191

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

Aliases

Subgroups

7122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542387);