Finite Group Databasebeta

?

← Prev (#72325444) Next (#72325446) →

C₂×#1506701 #72325445

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

Aliases

Subgroups

50757 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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