Finite Group Databasebeta

?

← Prev (#353664) Next (#353666) →

C₂×#10868 #353665

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

Aliases

Subgroups

2122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

(1,2);(3,4)(5,6)(7,8)(9,18,21,14)(10,23)(11,27)(12,17)(13,16)(15,24)(19,33,35,37)(20,29,22,32)(25,30)(26,38)(28,34,31,36);(4,6)(7,9,12,22,13,21,11,20)(8,14,17,29,16,18,27,32)(10,19,25,36,26,35,24,34)(15,28,23,37,30,31,38,33);(7,10,11,24,13,26,12,25)(8,15,17,23,16,30,27,38)(9,19,20,34,21,35,22,36)(14,28,29,37,18,31,32,33)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260861);