Finite Group Databasebeta

?

← Prev (#611175) Next (#611177) →

C₂×#16599 #611176

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

Aliases

Subgroups

4982 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8,11,10)(9,13,14,12)(16,19)(17,21)(23,24,26,28)(25,27,29,30);(15,16)(17,20)(18,19)(21,22)(23,25,26,29)(24,27,28,30);(7,9,11,14)(8,12,10,13)(15,16)(17,22)(18,19)(20,21)(23,25)(24,27)(26,29)(28,30);(3,4)(5,6)(7,10,11,8)(9,13,14,12)(15,17,18,21)(16,20,19,22)(23,24)(25,27)(26,28)(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, 518372);