Finite Group Databasebeta

?

← Prev (#7626078) Next (#7626080) →

C₂×#34477 #7626079

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

Aliases

Subgroups

9318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7533275);