Finite Group Databasebeta

?

← Prev (#6380539) Next (#6380541) →

C₂×#22782 #6380540

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

Aliases

Subgroups

2142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6287736);