Finite Group Databasebeta

?

← Prev (#7702220) Next (#7702222) →

C₂×#45453 #7702221

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

Aliases

Subgroups

8768 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7609417);