Finite Group Databasebeta

?

← Prev (#493556) Next (#493558) →

C₂×#12752 #493557

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

Aliases

Subgroups

3140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,8,12,9,6,20,13)(5,14,18,28,19,32,17,31)(7,22,24,11,25,29,34,21)(10,23,27,16,15,33,26,30);(3,5)(4,10)(6,15)(7,23)(8,17)(9,19)(11,28)(12,26)(13,27)(14,29)(16,34)(18,20)(21,31)(22,32)(24,30)(25,33);(3,6)(4,9)(5,15)(7,21)(8,12)(10,19)(11,25)(13,20)(14,30)(16,32)(17,26)(18,27)(22,34)(23,31)(24,29)(28,33)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400753);