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C₂×#62752 #10586152

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

Aliases

Subgroups

31992 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10493348);