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C₂³×#35680 #72278337

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

Aliases

Subgroups

6080824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 22 points:

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

Conjugacy classes & character table

512 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((3,4)(7,8)(9,10)(11,12)(13,14)(15,16)(17,20)(18,22)(19,21), (7,8,9,10)(11,12,13,14), (15,17,19,22)(16,20,21,18), (17,22)(18,20), (11,12)(13,14)(15,18)(16,17)(19,20)(21,22), (7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,21)(20,22), (5,6), (1,2)(3,4)(5,6));