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C₂×#13175 #495046

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

Aliases

Subgroups

606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402242);