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C₂×#33388 #7622506

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

Aliases

Subgroups

3958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529702);