Finite Group Databasebeta

?

← Prev (#609055) Next (#609057) →

C₂×#15482 #609056

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

Aliases

Subgroups

4410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 516252);