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C₂×#33572 #7622902

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

Aliases

Subgroups

3739 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530098);