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C₂×#57188 #8100415

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

Aliases

Subgroups

7546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,7)(6,8)(9,10)(11,12)(13,17)(14,18)(15,16)(20,23)(21,25);(6,10)(8,9)(12,16)(13,18)(19,20,22,23)(21,26,25,24);(4,5)(8,9)(11,13)(12,14)(15,18)(16,17)(19,20,22,23)(21,24,25,26);(3,5,7,4)(6,9,10,8)(11,13)(12,14)(15,18)(16,17)(19,20)(21,24)(22,23)(25,26);(3,6)(4,8)(5,9)(7,10)(11,14)(12,13)(15,17)(16,18)(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, 8007611);