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C₂×#36366 #7630021

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

Aliases

Subgroups

7134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(11,12)(13,15)(14,17)(16,18)(19,20)(21,22)(23,25)(24,26);(3,4,6,8)(5,7,10,9)(11,13,16,17)(12,14,18,15)(19,21,24,23)(20,22,26,25);(3,4)(5,9)(6,8)(7,10)(11,14,16,15)(12,17,18,13)(19,22,24,25)(20,23,26,21);(3,5)(4,7)(6,10)(8,9)(11,12)(13,14)(15,17)(16,18)(19,23,24,21)(20,25,26,22);(3,4)(5,9)(6,8)(7,10)(11,15,16,14)(12,13,18,17)(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, 7537217);