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C₂×#1269275 #72296261

• 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:

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