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C₂³×#3519 #72289352

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

Aliases

Subgroups

556709 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

352 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((7,8,12,11)(9,10,14,13), (3,4)(7,9)(8,13)(10,11)(12,14), (7,10,12,13)(8,14,11,9)(15,16,18,20)(17,21,22,19), (8,11)(10,13)(15,16)(17,21)(18,20)(19,22), (7,9)(8,10)(11,13)(12,14)(15,16)(17,21)(18,20)(19,22), (7,11,12,8)(9,10,14,13)(15,17,18,22)(16,19,20,21), (5,6), (1,2)(3,4)(5,6));