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C₂×#72250253 #72334439

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

Aliases

Subgroups

4681192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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