Finite Group Databasebeta

?

← Prev (#10577192) Next (#10577194) →

C₂×#61593 #10577193

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

Aliases

Subgroups

7976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10484389);