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C₂×#24450 #6437824

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

Aliases

Subgroups

5640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345020);