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C₄×#3022 #6372708

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

Aliases

Subgroups

4559 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279904);