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C₂×#18066 #6345106

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

Aliases

Subgroups

2106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252302);