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C₂×#20147 #6359482

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

Aliases

Subgroups

1698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,9,7)(5,12,14,18)(6,11,8,15)(10,17,16,13)(19,20,24,27)(21,25,23,32)(22,29,31,33)(26,30,34,28);(3,5,9,14)(4,10,7,16)(6,13,8,17)(11,18,15,12)(19,21,24,23)(20,25,27,32)(22,30,31,28)(26,29,34,33);(3,6,9,8)(4,11,7,15)(5,13,14,17)(10,18,16,12)(19,22)(20,26)(21,28)(23,30)(24,31)(25,33)(27,34)(29,32);(3,7,9,4)(5,12,14,18)(6,15,8,11)(10,17,16,13)(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, 6266678);