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C₂⁶×M₁₆ #72313894

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

Aliases

Subgroups

1012373 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 20 points:

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

Conjugacy classes & character table

640 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((13,14,15,18,16,17,19,20), (1,2), (3,4), (5,6), (7,8), (9,10), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(14,17)(18,20), (11,12));