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C₂×#18423 #6347014

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

Aliases

Subgroups

3018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6254210);