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C₂×#19758 #6358096

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

Aliases

Subgroups

2165 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6265292);