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C₂×#59442 #7666490

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

Aliases

Subgroups

6314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573686);