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C₂×#18533 #6348079

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

Aliases

Subgroups

4164 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6255275);