Finite Group Databasebeta

?

← Prev (#6376399) Next (#6376401) →

C₂×#22265 #6376400

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

Aliases

Subgroups

2874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

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, 6283596);