Finite Group Databasebeta

?

← Prev (#72325570) Next (#72325572) →

C₂×#2119238 #72325571

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

Aliases

Subgroups

42061 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

160 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((4,6)(11,12)(13,16)(14,17)(15,18)(19,20)(21,24)(22,23)(25,26), (4,6)(7,8)(9,10)(11,13)(12,15)(14,18)(16,17)(20,23)(21,25), (7,8)(9,10)(19,20,22,23)(21,24,25,26), (4,6)(8,10)(11,13)(12,16)(14,18)(15,17)(19,20)(21,26)(22,23)(24,25), (1,2), (3,4)(5,6)(7,8)(9,10)(11,12)(13,15)(14,17)(16,18)(19,21)(20,24)(22,25)(23,26));