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C₂×#72335118 #72335187

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

Aliases

Subgroups

915390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

368 conjugacy classes. The character table is too large to display.

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