Finite Group Databasebeta

?

← Prev (#493739) Next (#493741) →

C₂×#12810 #493740

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

Aliases

Subgroups

1108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400936);