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C₂×#57643 #8101443

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

Aliases

Subgroups

6556 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8008639);