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C₂×#2121549 #72294548

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

Aliases

Subgroups

47689 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

160 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((7,8,9,10)(11,12)(13,16)(14,17)(15,18)(19,20)(21,22)(23,25)(24,26), (7,8)(9,10)(11,13,14,18)(12,15,17,16)(19,20)(21,24)(22,26)(23,25), (4,6)(8,10)(13,18)(15,16)(19,21,23,26)(20,24,25,22), (7,8,9,10)(11,13)(12,16)(14,18)(15,17)(19,21)(20,22)(23,26)(24,25), (3,4)(5,6)(7,8)(9,10)(11,12)(13,16)(14,17)(15,18)(19,22)(20,21)(23,24)(25,26), (1,2));