Finite Group Databasebeta

?

← Prev (#7633537) Next (#7633539) →

C₂²×#2764 #7633538

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

Aliases

Subgroups

7570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540734);