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C₂×#48235 #7703247

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

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, 7610443);