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C₂×#56308 #8099249

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

Aliases

Subgroups

6196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8006445);