Finite Group Databasebeta

?

← Prev (#72323908) Next (#72323910) →

C₂×#712406 #72323909

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

Aliases

Subgroups

50213 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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