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C₂×#62334 #10577626

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

Aliases

Subgroups

6910 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)(13,19)(14,21)(16,23)(18,24)(20,25)(22,26);(3,5)(4,7)(6,10)(8,9)(11,12)(13,20)(14,18)(15,17)(16,22)(19,25)(21,24)(23,26);(11,13,21,26,15,22,14,19)(12,16,24,25,17,20,18,23);(5,10)(7,9)(11,12)(13,16)(14,18)(15,17)(19,23)(20,22)(21,24)(25,26);(4,8)(7,9)(12,17)(16,20)(18,24)(23,25)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484822);