Finite Group Databasebeta

?

← Prev (#10586173) Next (#10586175) →

C₂×#62826 #10586174

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

Aliases

Subgroups

32526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10493370);