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C₂×#59403 #7665908

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

Aliases

Subgroups

6964 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573104);