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C₂×#11670 #481286

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

Aliases

Subgroups

937 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

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, 388482);