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C₂×#14589 #521070

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

Aliases

Subgroups

5330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 428266);