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D₅₃×#2262 #27542216

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 117 points:

(1,4,7,22)(2,9,13,12)(3,15,19,18)(5,20,26,53)(6,21,29,54)(8,30,32,40)(10,33,37,36)(11,34,39,27)(14,41,42,49)(16,43,46,45)(17,44,48,28)(23,50,56,55)(24,51,58,57)(25,52,59,62)(31,38,60,64)(35,47,61,63)(65,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,112,114,116,117,115,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67);(1,3)(2,8)(4,15)(5,24)(6,28)(7,19)(9,30)(10,35)(11,38)(12,40)(13,32)(14,23)(16,25)(17,21)(18,22)(20,51)(26,58)(27,31)(29,44)(33,47)(34,60)(36,63)(37,61)(39,64)(41,50)(42,56)(43,52)(45,62)(46,59)(48,54)(49,55)(53,57);(1,2)(3,14)(4,9)(5,23)(6,27)(7,13)(8,16)(10,25)(11,21)(12,22)(15,41)(17,47)(18,49)(19,42)(20,50)(24,38)(26,56)(28,35)(29,34)(30,43)(31,57)(32,46)(33,52)(36,62)(37,59)(39,54)(40,45)(44,61)(48,63)(51,60)(53,55)(58,64);(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)(112,113)(114,115)(116,117)

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 327692);