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C₂×#51439 #7706956

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

Aliases

Subgroups

5784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7614152);