Finite Group Databasebeta

?

← Prev (#72296047) Next (#72296049) →

C₂²×#4387614 #72296048

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

Aliases

Subgroups

780936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

320 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((6,8)(10,12)(13,14)(15,16)(17,18)(19,20)(22,25)(23,27), (5,6,7,8)(9,10)(11,12)(14,18)(16,19)(21,22,24,25)(23,26,27,28), (13,15)(14,19)(16,18)(17,20)(21,22)(23,26)(24,25)(27,28), (5,6)(7,8)(13,15)(14,16)(17,20)(18,19)(21,22)(23,26)(24,25)(27,28), (13,16)(14,20)(15,18)(17,19)(21,23)(22,26)(24,27)(25,28), (3,4), (1,2)(3,4));