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C₂×#36856 #7633965

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

Aliases

Subgroups

7332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541161);