Finite Group Databasebeta

?

← Prev (#7634008) Next (#7634010) →

C₂×#36842 #7634009

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

Aliases

Subgroups

6812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7541205);