Finite Group Databasebeta

?

← Prev (#7628020) Next (#7628022) →

C₂²×#2597 #7628021

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

Aliases

Subgroups

8686 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535217);