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C₂×#12768 #493592

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

Aliases

Subgroups

2484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400788);