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C₂×#31394 #7504591

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

Aliases

Subgroups

2540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7411787);