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C₂×#52718 #8092490

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

Aliases

Subgroups

6352 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

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, 7999686);