Finite Group Databasebeta

?

← Prev (#6348083) Next (#6348085) →

C₂×#18538 #6348084

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

Aliases

Subgroups

3010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

(1,2);(3,4,8,12)(5,13,15,18)(6,11,7,10)(9,16,17,14)(19,20,25,30)(21,27,32,33)(22,26,31,34)(23,29,24,28);(3,5)(4,9)(6,14)(7,16)(8,15)(10,13)(11,18)(12,17)(19,21,25,32)(20,26,30,34)(22,23,31,24)(27,28,33,29);(19,22)(20,27)(21,23)(24,32)(25,31)(26,28)(29,34)(30,33);(3,6,8,7)(4,10,12,11)(5,14,15,16)(9,13,17,18)(19,23,25,24)(20,28,30,29)(21,31,32,22)(26,33,34,27)

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, 6255280);