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C₂×#53461 #8103380

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

Aliases

Subgroups

7364 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)(19,20,23,25)(21,22,26,24);(4,5)(8,9)(11,12)(13,17)(14,15)(16,18)(19,21,23,26)(20,24,25,22);(12,15)(16,17)(20,25)(22,24);(3,5,7,4)(6,9,10,8)(11,12)(13,16)(14,15)(17,18)(19,22,23,24)(20,21,25,26);(3,6)(4,8)(5,9)(7,10)(11,13)(12,16)(14,18)(15,17)(19,21)(20,24)(22,25)(23,26)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8010576);