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C₂×#43090 #7667281

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

Aliases

Subgroups

7016 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7574477);