Finite Group Databasebeta

?

← Prev (#72296844) Next (#72296846) →

C₂×#546217 #72296845

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

Aliases

Subgroups

41785 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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((8,10)(12,15)(16,18)(19,20)(21,25)(22,23)(24,26), (7,8)(9,10)(13,17)(16,18), (8,10)(12,15)(16,18)(20,23)(21,26), (7,8)(9,10)(11,12)(13,18)(14,15)(16,17)(19,20)(21,24)(22,23)(25,26), (3,4,5,6)(11,13)(12,16)(14,17)(15,18)(19,21,22,26)(20,24,23,25), (1,2));