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C₂×#17673 #6343795

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

Aliases

Subgroups

3192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

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, 6250991);