Finite Group Databasebeta

?

← Prev (#514019) Next (#514021) →

C₂×#13853 #514020

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

Aliases

Subgroups

6634 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421216);