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C₄×#1757 #353207

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

Aliases

Subgroups

1824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 260403);