Finite Group Databasebeta

?

← Prev (#10576041) Next (#10576043) →

C₂²×#3268 #10576042

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

Aliases

Subgroups

11502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

(1,2);(3,4);(5,6)(7,8)(10,14)(12,20)(15,21)(16,17)(18,24)(22,23);(9,10,13,17)(11,15,19,23)(12,16,20,14)(18,22,24,21);(6,8)(9,11,13,19)(10,15,17,23)(12,18,20,24)(14,21,16,22);(10,16)(12,20)(14,17)(15,22)(18,24)(21,23)

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, 10483238);