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C₂×#13215 #495142

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

Aliases

Subgroups

1286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402338);