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C₂×#20580 #6370682

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

Aliases

Subgroups

18514 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6277878);