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C₂×Q₃₂×C₃₇ #14557172

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 71 points:

(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71);(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18)(19,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20);(3,19,11,27)(4,20,12,28)(5,21,13,29)(6,22,14,30)(7,23,15,31)(8,24,16,32)(9,25,17,33)(10,26,18,34)

Conjugacy classes & character table

814 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 188);