Finite Group Databasebeta

?

← Prev (#6348043) Next (#6348045) →

C₂²×#1652 #6348044

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

Aliases

Subgroups

3194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 28 points:

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

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, 6255240);