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D₄₇×#3417 #27122799

• supersolvable
• metabelian
• solvable
• monomial
• stem
• ambivalent

Aliases

Splittings

Subgroups

2022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 111 points:

(4,18)(9,32)(14,42)(19,46)(20,47)(29,55)(33,57)(34,51)(40,62)(43,54)(44,52)(48,61)(49,64)(50,58)(56,60)(59,63)(65,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67);(1,4)(2,9)(3,14)(5,19)(6,20)(7,18)(8,29)(10,33)(11,34)(12,32)(13,40)(15,43)(16,44)(17,42)(21,48)(22,49)(23,47)(24,50)(25,46)(26,51)(27,52)(28,54)(30,56)(31,55)(35,58)(36,59)(37,57)(38,60)(39,61)(41,62)(45,63)(53,64);(1,3,7,17)(2,8,12,31)(4,14,18,42)(5,22,25,53)(6,27,23,16)(9,29,32,55)(10,36,37,45)(11,38,26,30)(13,39,41,21)(15,35,28,24)(19,49,46,64)(20,52,47,44)(33,59,57,63)(34,60,51,56)(40,61,62,48)(43,58,54,50);(1,2,7,12)(3,13,17,41)(4,9,18,32)(5,21,25,39)(6,26,23,11)(8,28,31,15)(10,35,37,24)(14,40,42,62)(16,45,27,36)(19,48,46,61)(20,51,47,34)(22,38,53,30)(29,54,55,43)(33,58,57,50)(44,63,52,59)(49,60,64,56);(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)

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, 1076089);