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C₂³×#3542 #72289445

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

Aliases

Subgroups

521533 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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