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C₂×#72236233 #72334565

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

Aliases

Subgroups

1542648 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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