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C₂×#36351 #7630005

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

Aliases

Subgroups

5832 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537201);