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C₂×#15955 #609888

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

Aliases

Subgroups

4810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 517084);