Finite Group Databasebeta

?

← Prev (#10576203) Next (#10576205) →

C₂×#61374 #10576204

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

Aliases

Subgroups

6506 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4,7,6)(5,9,10,8)(11,12,16,20)(13,17,22,26)(14,19,15,24)(18,23,25,21);(3,5,7,10)(4,8,6,9)(11,13)(12,17)(14,23)(15,21)(16,22)(18,24)(19,25)(20,26);(11,13)(12,18)(14,21)(15,23)(16,22)(17,24)(19,26)(20,25);(3,6,7,4)(5,8,10,9);(11,14,16,15)(12,19,20,24)(13,21,22,23)(17,18,26,25)

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, 10483400);