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C₂×#775096 #72294809

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

Aliases

Subgroups

51091 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)(13,16)(14,15)(17,18)(19,20,22,25)(21,23,26,24);(3,4)(5,6)(7,8)(9,10)(13,17)(16,18)(19,21,22,26)(20,23,25,24);(3,4)(5,6)(8,10)(12,15)(13,17)(19,21,22,26)(20,24,25,23);(4,6)(7,8)(9,10)(11,12)(13,16)(14,15)(17,18)(19,21)(20,24)(22,26)(23,25);(3,4)(5,6)(11,13)(12,16)(14,17)(15,18)(19,20)(21,23)(22,25)(24,26);(1,2)

Conjugacy classes & character table

196 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)(13,16)(14,15)(17,18)(19,20,22,25)(21,23,26,24), (3,4)(5,6)(7,8)(9,10)(13,17)(16,18)(19,21,22,26)(20,23,25,24), (3,4)(5,6)(8,10)(12,15)(13,17)(19,21,22,26)(20,24,25,23), (4,6)(7,8)(9,10)(11,12)(13,16)(14,15)(17,18)(19,21)(20,24)(22,26)(23,25), (3,4)(5,6)(11,13)(12,16)(14,17)(15,18)(19,20)(21,23)(22,25)(24,26), (1,2));