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C₂×#12706 #493389

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

Aliases

Subgroups

3458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400585);