Finite Group Databasebeta

?

← Prev (#495226) Next (#495228) →

C₂×#13243 #495227

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

Aliases

Subgroups

1080 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 66 points:

(1,2);(3,4)(5,17,22,41)(6,24)(7,14)(8,31)(9,33)(10,16)(11,20,36,29)(12,26)(13,18)(15,32)(19,34,49,60)(21,37,45,59)(23,35,51,44)(25,53)(27,38)(28,55)(30,42)(39,57)(40,46)(43,63,62,48)(47,64,56,52)(50,66,65,61)(54,58);(3,5,18,45,32,51,7,29,10,22,8,21,9,23,30,20)(4,11,14,35,33,59,13,41,16,36,42,44,15,37,31,17)(6,19,46,63,58,65,25,56,28,49,26,48,27,50,57,47)(12,34,24,52,53,66,38,62,40,60,55,64,39,61,54,43);(3,6,7,25,9,27,18,46,10,28,30,57,32,58,8,26)(4,12,31,54,15,39,42,55,16,40,13,38,33,53,14,24)(5,19,29,56,23,50,45,63,22,49,20,47,51,65,21,48)(11,34,17,43,37,61,44,64,36,60,41,62,59,66,35,52)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402423);