Finite Group Databasebeta

?

← Prev (#8103730) Next (#8103732) →

C₂×#54190 #8103731

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

Aliases

Subgroups

6428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

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, 8010927);