Finite Group Databasebeta

?

← Prev (#10585986) Next (#10585988) →

C₂²×#3512 #10585987

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

Aliases

Subgroups

35058 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 28 points:

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

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, 10493183);