Finite Group Databasebeta

?

← Prev (#72295208) Next (#72295210) →

C₂×#617875 #72295209

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

Aliases

Subgroups

82645 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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((7,8)(9,10)(12,15)(16,18)(19,20)(21,26)(22,24)(23,25), (7,8)(9,10)(19,21,23,22)(20,24,25,26), (4,6)(8,10)(12,15)(13,17)(19,22,23,21)(20,24,25,26), (3,4)(5,6)(7,8)(9,10)(11,12,14,15)(13,16,17,18), (11,13)(12,16)(14,17)(15,18)(19,20)(21,24)(22,26)(23,25), (1,2));