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C₂×#62827 #10586175

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

Aliases

Subgroups

32322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,12)(6,7)(8,9)(10,15)(11,16)(13,18)(14,17)(20,24)(22,29)(25,30)(28,33);(4,9)(6,11)(10,12)(13,17)(21,27)(25,30)(28,33)(32,34);(3,4,8,9)(5,10,15,12)(6,7,11,16)(13,14,17,18)(19,20,23,24)(21,25,27,30)(22,26,29,31)(28,32,33,34);(3,5,8,15)(4,10,9,12)(6,13,11,17)(7,14,16,18);(3,6,8,11)(4,7,9,16)(5,13,15,17)(10,14,12,18)(19,21)(20,25)(22,28)(23,27)(24,30)(26,32)(29,33)(31,34);(3,7)(4,11)(5,14)(6,9)(8,16)(10,17)(12,13)(15,18)(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, 10493371);