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C₂×#21785 #6374200

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

Aliases

Subgroups

4342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6281396);