Finite Group Databasebeta

?

← Prev (#6437745) Next (#6437747) →

C₂×#24396 #6437746

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

Aliases

Subgroups

4940 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4)(5,6)(11,12,17,23,16,14,15,19)(13,18,24,26,21,20,22,25);(4,6)(7,8)(9,10)(11,13)(12,18)(14,20)(15,22)(16,21)(17,24)(19,25)(23,26);(8,10)(11,14,16,12)(13,20,21,18)(15,19,17,23)(22,25,24,26);(4,6)(13,21)(18,20)(22,24)(25,26)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344942);