← Prev (#34209309) Next (#34209311) →
Aliases
Splittings
Subgroups
142 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 143 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);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(81,87)(82,93)(83,94)(84,99)(85,103)(88,89)(90,115)(91,117)(92,109)(95,125)(96,128)(97,121)(98,106)(100,134)(101,124)(102,107)(104,132)(105,108)(110,130)(111,129)(112,114)(113,136)(116,140)(118,119)(120,126)(122,123)(127,143)(131,138)(133,137)(135,139)(141,142);(80,81)(82,87)(83,98)(84,102)(85,105)(86,92)(88,93)(89,94)(90,99)(91,103)(95,115)(96,117)(97,109)(100,133)(101,131)(104,135)(106,119)(107,118)(108,126)(110,125)(111,128)(112,121)(113,134)(114,124)(116,132)(120,136)(122,130)(123,129)(127,140)(137,143)(138,142)(139,141)
Conjugacy classes & character table
1435 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90609);
Finite Group Databasebeta