Finite Group Databasebeta

?

← Prev (#10576871) Next (#10576873) →

C₂×#61554 #10576872

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

Aliases

Subgroups

6824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484068);