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C₂×#46199 #7702753

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

Aliases

Subgroups

7046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7609949);