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C₂×#7648640 #72267492

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

Aliases

Subgroups

112109 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

GAP

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

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