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C₂×#53167 #8105654

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

Aliases

Subgroups

7202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8012850);