Finite Group Databasebeta

?

← Prev (#72331949) Next (#72331951) →

C₂×#8272322 #72331950

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

Aliases

Subgroups

At least 9766 conjugacy classes of subgroups; only the 29501 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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