Finite Group Databasebeta

?

← Prev (#72331269) Next (#72331271) →

C₂×#72233780 #72331270

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

Aliases

Subgroups

4825672 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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

Conjugacy classes & character table

392 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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