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C₂×#72298082 #72299564

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

Aliases

Subgroups

At least 8852 conjugacy classes of subgroups; only the 38208 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

296 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)(12,14)(16,20)(17,18), (4,6)(11,12)(13,14)(15,16)(17,21)(18,22)(19,20), (8,10)(15,17)(16,21)(18,19)(20,22), (3,4,5,6)(7,8)(9,10)(17,18)(21,22), (3,4)(5,6)(15,18,19,17)(16,21,20,22), (3,4)(5,6)(15,16)(17,22)(18,21)(19,20), (1,2));