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C₂×#44823 #7669208

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

Aliases

Subgroups

6186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7576404);