Finite Group Databasebeta

?

← Prev (#7700599) Next (#7700601) →

C₂×#46837 #7700600

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

Aliases

Subgroups

6438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

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, 7607796);