Finite Group Databasebeta

?

← Prev (#6434125) Next (#6434127) →

C₂×#30056 #6434126

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

Aliases

Subgroups

1974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6341322);