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C₂×#33329 #7622422

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

Aliases

Subgroups

2146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529618);