Finite Group Databasebeta

?

← Prev (#27542198) Next (#27542200) →

D₅₃×#2258 #27542199

• 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:

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

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 327675);