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C₄×#2916 #6369939

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

Aliases

Subgroups

3004 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6277135);