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C₂×#31389 #7504602

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

Aliases

Subgroups

2626 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)(21,26)(22,30)(23,25)(24,27)(28,34)(29,32)(31,33);(3,5,7,4)(6,9,10,8)(11,13,14,17)(12,15,16,18)(20,25)(21,28)(22,24)(26,33)(29,31)(32,34);(3,6,7,10)(4,8,5,9)(12,16)(15,18)(19,21)(20,26)(22,28)(23,29)(24,31)(25,32)(27,33)(30,34);(4,5)(8,9)(12,16)(15,18)(19,22,23,24)(20,27,25,30)(21,28,29,31)(26,33,32,34)

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, 7411798);