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C₂×#36169 #7629805

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

Aliases

Subgroups

7188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537001);