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C₂×#45473 #7702192

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

Aliases

Subgroups

7690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7609388);