← Prev (#27156497) Next (#27156499) →
Aliases
Splittings
Subgroups
1408 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 129 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(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)(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);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(101,112)(105,119)(109,123)(113,125)(117,128)(120,126)(122,129)(124,127);(98,101)(99,105)(100,109)(102,113)(103,112)(104,117)(106,120)(107,119)(108,122)(110,124)(111,123)(114,126)(115,127)(116,125)(118,128)(121,129);(98,100,103,111)(99,104,107,118)(101,109,112,123)(102,115,116,110)(105,117,119,128)(106,121,114,108)(113,127,125,124)(120,129,126,122);(98,99,103,107)(100,108,111,121)(101,105,112,119)(102,114,116,106)(104,115,118,110)(109,122,123,129)(113,126,125,120)(117,127,128,124)
Conjugacy classes & character table
1100 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 19272);
Finite Group Databasebeta