Finite Group Databasebeta

?

← Prev (#7706562) Next (#7706564) →

C₂×#51023 #7706563

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

Aliases

Subgroups

7766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7613759);