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C₂×#612625 #72323914

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

Aliases

Subgroups

70241 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((20,23)(24,26), (4,6)(8,10)(11,12,14,16)(13,15,17,18)(20,23)(21,25), (7,8)(9,10)(19,20,22,23)(21,24,25,26), (3,4)(5,6)(7,8)(9,10)(11,12)(13,15)(14,16)(17,18), (1,2), (3,4)(5,6)(7,8)(9,10)(11,13,14,17)(12,15,16,18)(19,21,22,25)(20,24,23,26));