Finite Group Databasebeta

?

← Prev (#7708155) Next (#7708157) →

C₂×#52071 #7708156

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

Aliases

Subgroups

8522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7615352);