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C₂×#18154 #6346398

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

Aliases

Subgroups

3102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6253594);