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C₂×#33362 #7622465

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

Aliases

Subgroups

4234 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)(8,13,22,24)(9,14)(10,17,25,21)(16,26)(18,27,32,34)(19,28)(20,29)(23,30,33,31);(3,5,9,7)(4,10,14,25)(6,16,19,20)(8,21,22,17)(11,23,28,33)(12,24,15,13)(18,31,32,30)(26,27,29,34);(3,6,9,19)(4,11,14,28)(5,16,7,20)(8,18,22,32)(10,23,25,33)(12,29,15,26)(13,27,24,34)(17,30,21,31);(3,7,9,5)(4,12,14,15)(6,16,19,20)(8,21,22,17)(10,24,25,13)(11,26,28,29)(18,30,32,31)(23,27,33,34)

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, 7529661);