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C₂×#3564 #62734

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

Aliases

Subgroups

3299 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

(1,2);(3,4,7,8)(5,11,12,9)(6,14,15,10)(13,16,18,17)(19,20)(21,26)(22,27)(23,31)(24,25)(28,32)(29,30)(33,34);(4,8)(5,12)(10,14)(13,18)(20,25)(22,26)(28,31)(30,33);(3,5,7,12)(4,9,8,11)(6,13,15,18)(10,16,14,17)(19,21,24,27)(20,26,25,22)(23,29,32,34)(28,33,31,30);(3,4)(5,9)(6,10)(7,8)(11,12)(13,16)(14,15)(17,18)(19,22,24,26)(20,27,25,21)(23,30,32,33)(28,34,31,29);(3,6)(4,10)(5,13)(7,15)(8,14)(9,16)(11,17)(12,18)(19,23)(20,28)(21,29)(22,30)(24,32)(25,31)(26,33)(27,34)

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55722);