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C₂×#1419350 #72294005

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

Aliases

Subgroups

73423 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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