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C₂³×#3546 #72301669

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

Aliases

Subgroups

517029 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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