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C₂×#48161 #7703801

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

Aliases

Subgroups

6182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(11,12,15,16)(13,14,17,18)(19,20,24,22)(21,26,23,25);(3,4)(5,9)(6,10)(7,8)(11,12,15,16)(13,18,17,14)(20,22)(25,26);(4,8)(5,10)(12,16)(13,17)(19,21,24,23)(20,25,22,26);(3,5)(4,6)(7,10)(8,9)(11,13,15,17)(12,14,16,18)(19,22,24,20)(21,26,23,25);(3,6)(4,5)(7,9)(8,10)(11,14)(12,17)(13,16)(15,18)(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, 7610997);