Finite Group Databasebeta

?

← Prev (#6437492) Next (#6437494) →

C₂×#23854 #6437493

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

Aliases

Subgroups

6444 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344689);