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C₂×#613650 #72302750

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

Aliases

Subgroups

68361 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((1,2)(3,4)(5,6)(7,8,9,10)(12,15)(16,17)(19,20,23,24)(21,26,25,22), (4,6)(20,24)(21,25), (3,4)(5,6)(7,8)(9,10)(11,12,14,15)(13,17,18,16)(19,21)(20,22)(23,25)(24,26), (3,4)(5,6)(7,8)(9,10)(11,12,14,15)(13,17,18,16)(19,22,23,26)(20,25,24,21), (8,10)(11,12)(13,17)(14,15)(16,18)(19,22)(20,25)(21,24)(23,26), (3,4)(5,6)(7,8)(9,10)(11,13,14,18)(12,16,15,17)(19,20,23,24)(21,26,25,22));