Finite Group Databasebeta

?

← Prev (#72233731) Next (#72233733) →

C₂×#10575547 #72233732

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

Aliases

Subgroups

84933 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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