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C₂×#20757 #6371035

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

Aliases

Subgroups

2294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278231);