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C₂²×#1747 #6369778

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

Aliases

Subgroups

2810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6276974);