Finite Group Databasebeta

?

← Prev (#3451) Next (#3453) →

C₂×#540 #3452

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

Aliases

Subgroups

630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

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

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 2184);