Finite Group Databasebeta

?

← Prev (#72296052) Next (#72296054) →

C₂²×#576607 #72296053

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

Aliases

Subgroups

636456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 28 points:

(10,12)(15,19)(18,20)(24,28)(26,27);(5,6,8,7)(9,10)(11,12)(15,19)(18,20)(21,22,25,23)(24,26,28,27);(14,17)(18,20)(22,23)(26,27);(5,7,8,6)(13,14)(15,20)(16,17)(18,19)(21,23,25,22)(24,27,28,26);(13,15)(14,18)(16,19)(17,20)(21,24)(22,26)(23,27)(25,28);(3,4);(1,2)(3,4)

Conjugacy classes & character table

416 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((10,12)(15,19)(18,20)(24,28)(26,27), (5,6,8,7)(9,10)(11,12)(15,19)(18,20)(21,22,25,23)(24,26,28,27), (14,17)(18,20)(22,23)(26,27), (5,7,8,6)(13,14)(15,20)(16,17)(18,19)(21,23,25,22)(24,27,28,26), (13,15)(14,18)(16,19)(17,20)(21,24)(22,26)(23,27)(25,28), (3,4), (1,2)(3,4));