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C₂×#7626202 #72255584

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

Aliases

Subgroups

204517 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 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((1,2), (9,13)(12,14)(17,21)(20,22), (3,4,5,6)(8,11)(12,14)(16,19)(20,22), (15,16)(17,20)(18,19)(21,22), (15,17)(16,20)(18,21)(19,22), (7,8)(9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22), (7,9)(8,12)(10,13)(11,14)(15,17)(16,20)(18,21)(19,22));