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C₂³×#3508 #72301431

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

Aliases

Subgroups

547701 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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