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C₂×#23649 #6432192

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

Aliases

Subgroups

2810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

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, 6339388);