Finite Group Databasebeta

?

← Prev (#10575287) Next (#10575289) →

C₂²×#3168 #10575288

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

Aliases

Subgroups

7514 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)(13,14)(15,19)(16,23)(17,26)(18,21)(20,24)(22,27)(25,28);(6,9)(10,12)(13,15,18,17)(14,19,21,26)(16,22,25,24)(20,23,27,28);(13,16,17,24,18,25,15,22)(14,20,19,23,21,27,26,28);(5,7,8,11)(6,10,9,12)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482484);