Finite Group Databasebeta

?

← Prev (#7667675) Next (#7667677) →

C₂×#43494 #7667676

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

Aliases

Subgroups

8358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574872);