Finite Group Databasebeta

?

← Prev (#7629085) Next (#7629087) →

C₂×#35665 #7629086

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

Aliases

Subgroups

8182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536282);