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C₂×#35690 #7629326

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

Aliases

Subgroups

6336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,8)(6,9)(7,10)(11,12)(13,18)(14,16)(15,17)(20,23)(24,26);(3,4)(5,8)(6,9)(7,10)(11,13)(12,14)(15,16)(17,18)(19,20)(21,24)(22,23)(25,26);(3,5)(4,6)(7,9)(8,10)(11,12)(13,18)(14,16)(15,17);(3,5)(4,8)(6,10)(7,9)(11,14,15,18)(12,16,17,13);(3,6,7,8)(4,9,10,5)(11,12)(13,14)(15,17)(16,18)(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, 7536522);