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C₂×#51441 #7707012

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

Aliases

Subgroups

7230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7614208);