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C₂×#60751 #10575414

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

Aliases

Subgroups

8862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10482610);