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C₂×#17704 #6343970

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

Aliases

Subgroups

4510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6251166);