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C₂×#60342 #10574551

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

Aliases

Subgroups

6212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481747);