Finite Group Databasebeta

?

← Prev (#353514) Next (#353516) →

C₂×#10811 #353515

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

Aliases

Subgroups

1814 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260711);