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C₂×#33358 #7622461

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

Aliases

Subgroups

4334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529657);