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C₂×#59885 #7666740

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573936);