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C₂×#62372 #10578414

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

Aliases

Subgroups

6206 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)(21,27)(22,29)(24,30)(26,32)(28,33)(31,34);(3,5,7,13)(4,8,10,11)(6,14,15,12)(9,17,18,16)(19,20,23,25)(21,24,28,31)(22,26,29,32)(27,30,33,34);(19,21,22,27,23,28,29,33)(20,24,26,30,25,31,32,34);(3,6,7,15)(4,9,10,18)(5,12,13,14)(8,16,11,17);(4,10)(8,11)(9,18)(16,17)(20,25)(24,31)(26,32)(30,34)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485610);