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C₂×#13229 #495193

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

Aliases

Subgroups

1216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

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, 402389);