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C₂×#20401 #6369830

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

Aliases

Subgroups

4990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277026);