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C₂×#33351 #7622449

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

Aliases

Subgroups

4216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529645);