Finite Group Databasebeta

?

← Prev (#10577989) Next (#10577991) →

C₂×#61815 #10577990

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

Aliases

Subgroups

6510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485186);