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C₂×#62828 #10586176

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

Aliases

Subgroups

32360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10493372);