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C₂×#37989 #7635162

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

Aliases

Subgroups

6748 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542358);