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C₂×#1302675 #72299162

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

Aliases

Subgroups

40963 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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