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C₂×#1269265 #72294698

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

Aliases

Subgroups

51007 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

172 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((8,10)(11,12,15,13)(14,17,18,16)(19,20,24,23)(21,26,25,22), (7,8)(9,10)(12,13)(16,17)(19,21,24,25)(20,22,23,26), (4,6)(12,13)(14,18)(19,22,24,26)(20,21,23,25), (3,4)(5,6)(11,13,15,12)(14,16,18,17)(19,23,24,20)(21,22,25,26), (3,4)(5,6)(11,14)(12,16)(13,17)(15,18)(19,22)(20,25)(21,23)(24,26), (1,2));