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C₂×#36368 #7630023

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

Aliases

Subgroups

7074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537219);