Finite Group Databasebeta

?

← Prev (#72325421) Next (#72325423) →

C₂×#1515169 #72325422

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

Aliases

Subgroups

47099 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

148 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((7,8)(9,10)(11,12,14,16)(13,17,18,15)(20,23)(24,25), (3,4)(5,6)(19,20)(21,24)(22,23)(25,26), (4,6)(7,8)(9,10)(13,18)(15,17), (4,6)(7,8,9,10)(11,12)(13,15)(14,16)(17,18)(19,20)(21,25)(22,23)(24,26), (1,2), (3,4)(5,6)(7,8)(9,10)(11,13)(12,15)(14,18)(16,17)(19,21)(20,24)(22,26)(23,25));