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C₂×#72233528 #72298786

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

Aliases

Subgroups

993552 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)(12,14)(15,16)(17,20)(18,21)(19,22);(4,6)(8,10)(11,12)(13,14)(15,16)(17,19)(18,21)(20,22);(4,6)(7,8,9,10)(15,17,18,22)(16,19,21,20);(4,6)(7,8,9,10)(15,16)(17,19)(18,21)(20,22);(7,8)(9,10);(3,4)(5,6)(7,8)(9,10)(15,17)(16,20)(18,22)(19,21);(1,2)

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