Finite Group Databasebeta

?

← Prev (#353362) Next (#353364) →

C₂×#10778 #353363

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

Aliases

Subgroups

4022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260559);