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C₂×#48665 #7703312

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

Aliases

Subgroups

6802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610508);