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C₂×#22462 #6379194

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

Aliases

Subgroups

4552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6286390);