Finite Group Databasebeta

?

← Prev (#499074) Next (#499076) →

C₂×#13413 #499075

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

Aliases

Subgroups

1538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

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, 406271);