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C₂²×#2080 #6432191

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

Aliases

Subgroups

2854 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)(11,17,25,22)(16,31,19,30)(20,26)(21,27)(23,29)(24,33,35,32)(34,36);(5,7)(6,11)(8,19)(9,22)(10,18)(12,24)(13,28)(14,25)(15,29)(16,21)(17,23)(20,32)(26,31)(27,35)(30,36)(33,34);(5,8,9,20,10,21,23,34)(6,12,13,26,14,27,29,36)(7,16,17,32,18,19,22,33)(11,24,15,30,25,35,28,31)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339387);