Finite Group Databasebeta

?

← Prev (#6357261) Next (#6357263) →

C₂×#19688 #6357262

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

Aliases

Subgroups

2084 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6264458);