Finite Group Databasebeta

?

← Prev (#10576173) Next (#10576175) →

C₂×#61109 #10576174

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

Aliases

Subgroups

10260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10483370);