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C₂×#48642 #7703535

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

Aliases

Subgroups

6036 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,7,9)(5,10,6,8)(11,12)(13,17)(14,18)(15,16);(3,5,7,6)(4,8,9,10)(11,13)(12,14)(15,18)(16,17)(19,20)(21,25)(22,26)(23,24);(5,6)(8,10)(12,16)(13,18)(20,24)(21,26);(3,6,7,5)(4,8,9,10)(11,13)(12,17)(14,16)(15,18)(19,21)(20,22)(23,26)(24,25);(3,4)(5,10)(6,8)(7,9)(11,14,15,17)(12,13,16,18)(19,22)(20,21)(23,25)(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, 7610731);