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C₂×#15967 #609902

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

Aliases

Subgroups

5854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 517098);