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C₄×#504 #33325

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

Aliases

Subgroups

417 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 36 points:

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 26313);