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C₂×#3858085 #72294741

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

Aliases

Subgroups

47223 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

172 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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