Finite Group Databasebeta

?

← Prev (#495748) Next (#495750) →

C₄×#2201 #495749

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

Aliases

Subgroups

1113 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402945);