Finite Group Databasebeta

?

← Prev (#72296049) Next (#72296051) →

C₂²×#1082853 #72296050

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

Aliases

Subgroups

At least 7323 conjugacy classes of subgroups; only the 38784 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

344 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)(14,17)(18,20)(22,25)(23,27), (5,6)(7,8)(9,10)(11,12)(15,19)(18,20)(23,27)(26,28), (6,8)(14,17)(18,20)(21,22,24,25)(23,26,27,28), (5,6)(7,8)(13,14)(15,20)(16,17)(18,19)(21,22)(23,28)(24,25)(26,27), (13,15)(14,18)(16,19)(17,20)(21,23)(22,26)(24,27)(25,28), (3,4), (1,2)(3,4));