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C₂×#36531 #7630220

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

Aliases

Subgroups

7384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537416);