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C₂×#37307 #7634649

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

Aliases

Subgroups

6390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7541845);