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C₂×#20156 #6359494

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

Aliases

Subgroups

1648 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)(21,25)(22,29)(23,32)(24,27)(26,28)(30,34)(31,33);(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)(19,22,24,31)(20,26,27,34)(21,28,23,30)(25,33,32,29);(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, 6266690);