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C₂×#20141 #6359475

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

Aliases

Subgroups

1724 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6266671);