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C₂×#55679 #8098909

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

Aliases

Subgroups

5962 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)(13,17)(15,18)(19,20,22,24)(21,25,26,23);(3,4,6,8)(5,7,10,9)(11,12,14,16)(13,15,17,18)(21,26)(23,25);(11,13,14,17)(12,15,16,18)(19,21,22,26)(20,23,24,25);(3,4)(5,7)(6,8)(9,10)(11,13)(12,15)(14,17)(16,18)(19,20)(21,23)(22,24)(25,26);(3,5)(4,7)(6,10)(8,9)(11,12)(13,15)(14,16)(17,18)

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, 8006105);