Finite Group Databasebeta

?

← Prev (#493394) Next (#493396) →

C₂×#12708 #493395

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

Aliases

Subgroups

3448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400591);