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D₄₇×#3177 #27086114

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

1842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 87 points:

(1,3,4,7)(2,6,5,8)(11,20)(15,28)(19,34)(21,33)(27,39)(29,36)(32,40)(35,38)(41,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43);(9,12,23,30,14,25,13,24)(10,16,26,37,18,31,17,22)(11,19,33,38,20,34,21,35)(15,27,36,40,28,39,29,32);(2,5)(6,8)(9,11,14,20)(10,15,18,28)(12,19,25,34)(13,21,23,33)(16,27,31,39)(17,29,26,36)(22,32,37,40)(24,35,30,38);(1,2)(3,6)(4,5)(7,8)(9,10,14,18)(11,15,20,28)(12,22,25,37)(13,26,23,17)(16,30,31,24)(19,32,34,40)(21,36,33,29)(27,38,39,35);(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)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)

Conjugacy classes & character table

800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1039404);