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C₂×#59553 #7666482

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

Aliases

Subgroups

5832 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573678);