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C₂²×#13395 #72311694

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

Aliases

Subgroups

8309 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

(6,11)(7,15,17,29)(8,19)(9,20)(12,24,21,25)(13,27)(16,31)(18,33,32,30)(22,28)(26,36,34,35);(1,2);(1,2)(3,4)(5,6)(8,13)(9,14)(10,11)(16,22)(19,28)(20,23)(27,31);(3,4);(1,2)(3,4)(5,7,16,29,9,18,31,33,10,17,8,15,20,32,19,30)(6,12,22,24,14,26,27,35,11,21,13,25,23,34,28,36)

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((6,11)(7,15,17,29)(8,19)(9,20)(12,24,21,25)(13,27)(16,31)(18,33,32,30)(22,28)(26,36,34,35), (1,2), (1,2)(3,4)(5,6)(8,13)(9,14)(10,11)(16,22)(19,28)(20,23)(27,31), (3,4), (1,2)(3,4)(5,7,16,29,9,18,31,33,10,17,8,15,20,32,19,30)(6,12,22,24,14,26,27,35,11,21,13,25,23,34,28,36));