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C₂³×#3549 #72289451

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

Aliases

Subgroups

557373 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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