Finite Group Databasebeta

?

← Prev (#10586345) Next (#10586347) →

C₂×#63026 #10586346

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

Aliases

Subgroups

32558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 34 points:

(1,2);(3,4,8,10)(5,13,17,27)(6,12,18,24)(7,11,20,23)(9,14,22,16)(15,26,29,34)(19,25,31,33)(21,28,32,30);(3,5,7,16)(4,9,11,13)(6,15,19,30)(8,17,20,14)(10,22,23,27)(12,21,25,26)(18,29,31,28)(24,32,33,34);(4,10)(5,14)(9,13)(11,23)(12,24)(15,28)(16,17)(21,26)(22,27)(25,33)(29,30)(32,34);(4,11)(9,13)(10,23)(12,25)(21,26)(22,27)(24,33)(32,34);(3,6,7,19)(4,12,11,25)(5,15,16,30)(8,18,20,31)(9,21,13,26)(10,24,23,33)(14,28,17,29)(22,32,27,34);(6,18)(12,24)(15,29)(19,31)(21,32)(25,33)(26,34)(28,30)

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, 10493542);