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C₂×#62249 #10577531

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

Aliases

Subgroups

6906 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)(13,17)(14,21)(15,24)(16,19)(18,22)(20,25)(23,26);(3,5)(4,7)(6,10)(8,9)(11,13,16,15)(12,17,19,24)(14,20,23,22)(18,21,25,26);(11,14,13,20,16,23,15,22)(12,18,24,26,19,25,17,21);(5,10)(7,9)(11,13,16,15)(12,17,19,24)(14,20,23,22)(18,21,25,26);(4,8)(7,9)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484727);