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C₂×#62841 #10586192

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

Aliases

Subgroups

32316 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 34 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493388);