Finite Group Databasebeta

?

← Prev (#7636768) Next (#7636770) →

C₂×#39461 #7636769

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

Aliases

Subgroups

9092 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7543965);