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C₂×#1976 #21243

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

Aliases

Subgroups

737 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14231);