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C₂×#11604 #481072

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

Aliases

Subgroups

1024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 388268);