Finite Group Databasebeta

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C₂³×#3536 #72301666

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

Aliases

Subgroups

514605 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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