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C₂×#23431 #6431752

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

Aliases

Subgroups

7970 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)(13,21)(14,19)(15,18)(16,20)(17,22)(23,26)(24,25);(4,6)(7,8)(9,10)(11,13,16,24)(12,17,20,26)(14,23,15,22)(18,25,19,21);(8,10)(12,18)(14,15)(17,25)(19,20)(21,26)(22,23);(11,14,16,15)(12,19,20,18)(13,22,24,23)(17,25,26,21)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6338948);