Finite Group Databasebeta

?

← Prev (#7503877) Next (#7503879) →

C₂×#31250 #7503878

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

Aliases

Subgroups

2444 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7411074);