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C₂×#845801 #72334446

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

Aliases

Subgroups

71483 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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)(7,8)(9,10)(11,12)(13,15)(14,17)(16,18)(20,23)(24,26), (4,6)(7,8,9,10)(11,13,14,18)(12,15,17,16)(20,23)(21,25), (4,6)(8,10)(11,12,14,17)(13,16,18,15)(19,20,22,23)(21,26,25,24), (11,13)(12,16)(14,18)(15,17)(19,21)(20,24)(22,25)(23,26), (1,2), (3,4)(5,6)(7,8)(9,10)(11,12)(13,16)(14,17)(15,18)(19,21)(20,24)(22,25)(23,26));