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C₂×#16601 #611190

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

Aliases

Subgroups

5998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518386);