Finite Group Databasebeta

?

← Prev (#7633586) Next (#7633588) →

C₂²×#2808 #7633587

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

Aliases

Subgroups

8090 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540783);