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C₂×#51549 #7707419

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

Aliases

Subgroups

6522 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)(13,17)(14,15)(16,18)(19,20)(21,25)(22,24)(23,26);(4,7)(8,9)(11,13)(12,16)(14,17)(15,18)(19,20,22,24)(21,23,26,25);(13,18)(16,17)(19,21)(20,23)(22,26)(24,25);(3,4)(5,8)(6,7)(9,10)(11,13)(12,17)(14,16)(15,18)(19,20)(21,23)(22,24)(25,26);(3,5)(4,8)(6,10)(7,9)(11,14,15,12)(13,16,18,17)(19,21)(20,23)(22,26)(24,25)

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, 7614615);