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C₂×#18168 #6346422

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

Aliases

Subgroups

4176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6253618);