Finite Group Databasebeta

?

← Prev (#10574052) Next (#10574054) →

C₂²×#2889 #10574053

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

Aliases

Subgroups

22250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 36 points:

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

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481249);