Finite Group Databasebeta

?

← Prev (#7635656) Next (#7635658) →

C₂×#38087 #7635657

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

Aliases

Subgroups

8588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542853);