Finite Group Databasebeta

?

← Prev (#72332585) Next (#72332587) →

C₂×#570715 #72332586

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

Aliases

Subgroups

36125 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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