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C₂³×#3534 #72289442

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

Aliases

Subgroups

523989 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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