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C₂×#37165 #7634439

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

Aliases

Subgroups

6106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

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, 7541635);