Finite Group Databasebeta

?

← Prev (#7641186) Next (#7641188) →

C₂×#42673 #7641187

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

Aliases

Subgroups

9466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548383);