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C₂×#12715 #493415

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

Aliases

Subgroups

3386 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400611);