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C₂³×#3506 #72301671

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

Aliases

Subgroups

515549 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)(9,10,12,14)(15,16)(17,19)(18,20)(21,22);(7,8)(9,10)(11,13)(12,14)(16,17)(20,21);(7,9,11,12)(8,10,13,14)(15,17,19,16)(18,21,22,20);(7,10,11,14)(8,12,13,9);(7,8)(9,10)(11,13)(12,14)(15,18,19,22)(16,20,17,21)

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