Finite Group Databasebeta

?

← Prev (#7707885) Next (#7707887) →

C₂×#51901 #7707886

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

Aliases

Subgroups

8736 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7615082);