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C₂×#11769 #481727

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

Aliases

Subgroups

777 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 388923);