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C₂×#33704 #7623168

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

Aliases

Subgroups

2006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 7530364);