Finite Group Databasebeta

?

← Prev (#72302264) Next (#72302266) →

C₂×#7671277 #72302265

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

Aliases

Subgroups

123465 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

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