Finite Group Databasebeta

?

← Prev (#7622869) Next (#7622871) →

C₂×#33558 #7622870

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

Aliases

Subgroups

3882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530066);