Finite Group Databasebeta

← Group #14285241

Character table — Group #14285241

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222444446688888888888810101010121212121216161616161616202020202424242424242440404040404040404040404040606080120120120120120
order122236664510101022210101010121520203030304444410101010630303030606012121212210101010202028888242424242424242444628888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111111-1ii−i−iiiii−i−i−i−i-1-1-1-1ii−i−i
χ4111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111111-1−i−iii−i−i−i−iiiii-1-1-1-1−i−iii
χ5111111111111111-1-1-1-1-11111111111111111-1-1-1-1-1111111-1-1-1-1-111-11-11-111-1-111-1-111-1-11-11-1
χ6111111111111111-1-1-1-1-11111111111111111-1-1-1-1-1111111-1-1-1-1-111-1-11-11-1-111-1-11111-1-1-11-11
χ7111111111111111-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1111i−i−iiii−i−i−i−iii-1-111i−i−ii
χ8111111111111111-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1111−iii−i−i−iiiii−i−i-1-111−iii−i
χ91111111111111-1-11111111111111111-1-1-1-1-111111111111-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1
χ101111111111111-1-11111111111111111-1-1-1-1-111111111111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111
χ111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i11-11−i−iii
χ121111111111111-1-1111111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii11-11ii−i−i
χ131111111111111-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-11-11-111-1-111-1-1-1-1-11-11-11
χ141111111111111-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-11-11-1-111-1-111-1-1-111-11-1
χ151111111111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-11i−i−iiii−i−i−i−iii111-1−iii−i
χ161111111111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-11−iii−i−i−iiiii−i−i111-1i−i−ii
χ1722222222-222222200000-22-2-22222-22-2-2222200000-2-22-22-200000-2-200000000000002-2000000
χ1822222222-222222200000-22-2-2222-22-22-2222200000-2-2-22-2200000-2-20000000000000-22000000
χ1922222222-22222-2-200000-22-2-22222-22-22-2-2-2-200000-2-22-22-200000220000000000000-22000000
χ2022222222-22222-2-200000-22-2-2222-22-222-2-2-2-200000-2-2-22-22000002200000000000002-2000000
χ212222-1-1-1-1222220022222-1-122-1-1-1222200000-1-1-1-1-1-1-1-1-1-1-1000000022222-1-1-1-1-1-1-1-100-100000
χ222222-1-1-1-1222220022222-1-122-1-1-1222200000-1-1-1-1-1-1-1-1-1-1-100000002-2-2-2-21111111100-100000
χ232222-1-1-1-1222220022222-1-122-1-1-1-2-2-2-200000-1-1-1-1-1-1-111110000000-22i2i−2i−2i−i−i−i−iiiii00100000
χ242222-1-1-1-1222220022222-1-122-1-1-1-2-2-2-200000-1-1-1-1-1-1-111110000000-2−2i−2i2i2iiiii−i−i−i−i00100000
χ252222-1-1-1-12222200-2-2-2-2-2-1-122-1-1-122220000011111-1-1-1-1-1-10000000-22-22-2-1-111-1-11100100000
χ262222-1-1-1-12222200-2-2-2-2-2-1-122-1-1-122220000011111-1-1-1-1-1-10000000-2-22-2211-1-111-1-100100000
χ272222-1-1-1-12222200-2-2-2-2-2-1-122-1-1-1-2-2-2-20000011111-1-11111000000022i−2i−2i2i−i−iiiii−i−i00-100000
χ282222-1-1-1-12222200-2-2-2-2-2-1-122-1-1-1-2-2-2-20000011111-1-1111100000002−2i2i2i−2iii−i−i−i−iii00-100000
χ29444444444-1-1-1-1444-1-1-1-14-1-1-1-1-1-100004-1-1-1-14-1-1-1-1-1-100004-1-1-1-1-1-1000000000000000000000
χ30444444444-1-1-1-144-411114-1-1-1-1-1-100004-1-1-1-1-41111-1-10000-41111-1-1000000000000000000000
χ31444444444-1-1-1-1-4-44-1-1-1-14-1-1-1-1-1-10000-411114-1-1-1-1-1-10000-4111111000000000000000000000
χ32444444444-1-1-1-1-4-4-411114-1-1-1-1-1-10000-41111-41111-1-100004-1-1-1-111000000000000000000000
χ3344444444-4-1-1-1-1440−5−555-4-111-1-1-10000-4-1-1-1-10−5−5551100000−5−55511000000000000000000000
χ3444444444-4-1-1-1-144055−5−5-4-111-1-1-10000-4-1-1-1-1055−5−5110000055−5−511000000000000000000000
χ3544444444-4-1-1-1-1-4-40−5−555-4-111-1-1-10000411110−5−555110000055−5−5-1-1000000000000000000000
χ3644444444-4-1-1-1-1-4-4055−5−5-4-111-1-1-1000041111055−5−51100000−5−555-1-1000000000000000000000
χ374444-2-2-2-2-4444400000002-2-4-4-2-2-24-44-4000000000022-22-220000000000000000000000000000
χ384444-2-2-2-2-4444400000002-2-4-4-2-2-2-44-440000000000222-22-20000000000000000000000000000
χ3944-4-444-4-404-4-444-4000000400-4-440000044-4-4000000000000000000000000000000000000000
χ4044-4-444-4-404-4-44-44000000400-4-4400000-4-444000000000000000000000000000000000000000
χ4144-4-444-4-40-111-14-40ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ1160-1−5511-100000-1-1110ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−5500000ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−55000000000000000000000
χ4244-4-444-4-40-111-14-40−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ1160-1−5511-100000-1-1110−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−5500000−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−55000000000000000000000
χ4344-4-444-4-40-111-14-40ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ1160-15−511-100000-1-1110ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ1165−500000ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ1165−5000000000000000000000
χ4444-4-444-4-40-111-14-40−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ1160-15−511-100000-1-1110−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ1165−500000−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ1165−5000000000000000000000
χ4544-4-444-4-40-111-1-440ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ1160-1−5511-10000011-1-10ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−5500000−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ1165−5000000000000000000000
χ4644-4-444-4-40-111-1-440−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ1160-1−5511-10000011-1-10−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−5500000ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ1165−5000000000000000000000
χ4744-4-444-4-40-111-1-440ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ1160-15−511-10000011-1-10ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ1165−500000−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−55000000000000000000000
χ4844-4-444-4-40-111-1-440−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ1160-15−511-10000011-1-10−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ1165−500000ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−55000000000000000000000
χ494-44-44-44-4044-4-4000000004004-4-4040-40000000000000-4040000000000000000000000000000
χ504-44-44-44-4044-4-4000000004004-4-40-404000000000000040-40000000000000000000000000000
χ514-44-4-22-22044-4-400000000-200-222040-4000000000000020-2000000000000−i6i600−i6i60000000000
χ524-44-4-22-22044-4-400000000-200-222040-4000000000000020-2000000000000i6−i600i6−i60000000000
χ534-44-4-22-22044-4-400000000-200-2220-4040000000000000-2020000000000006−600−660000000000
χ544-44-4-22-22044-4-400000000-200-2220-4040000000000000-202000000000000−66006−60000000000
χ554-4-444-4-4404-44-400000000400-44-440-40000000000000-40400000000000000000000000000000
χ564-4-444-4-4404-44-400000000400-44-4-404000000000000040-400000000000000000000000000000
χ574-4-44-222-204-44-400000000-2002-2240-4000000000000020-2000000000000000−i6i600−i6i600000000
χ584-4-44-222-204-44-400000000-2002-2240-4000000000000020-2000000000000000i6−i600i6−i600000000
χ594-4-44-222-204-44-400000000-2002-22-4040000000000000-2020000000000000006−600−6600000000
χ604-4-44-222-204-44-400000000-2002-22-4040000000000000-202000000000000000−66006−600000000
χ618888-4-4-4-48-2-2-2-2008-2-2-2-2-41-2-2111000000000-411111100000000000000000000000000000000
χ628888-4-4-4-48-2-2-2-200-82222-41-2-21110000000004-1-1-1-11100000000000000000000000000000000
χ638888-4-4-4-4-8-2-2-2-2000−25−2525254122111000000000055−5−5-1-100000000000000000000000000000000
χ648888-4-4-4-4-8-2-2-2-20002525−25−2541221110000000000−5−555-1-100000000000000000000000000000000
χ6588-8-8-4-44408-8-8800000000-40044-4000000000000000000000000000000000000000000000000
χ6688-8-8-4-4440-222-20002ζ4−2ζ28+2ζ44+2ζ52−2ζ68−2ζ76+2ζ92−2ζ116−2ζ4+2ζ28−2ζ44−2ζ52+2ζ68+2ζ76−2ζ92+2ζ1162ζ4+2ζ28+2ζ44−2ζ52+2ζ68−2ζ76−2ζ92−2ζ116−2ζ4−2ζ28−2ζ44+2ζ52−2ζ68+2ζ76+2ζ92+2ζ11601−2525-1-110000000000−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ1165−500000000000000000000000000000000
χ6788-8-8-4-4440-222-2000−2ζ4+2ζ28−2ζ44−2ζ52+2ζ68+2ζ76−2ζ92+2ζ1162ζ4−2ζ28+2ζ44+2ζ52−2ζ68−2ζ76+2ζ92−2ζ116−2ζ4−2ζ28−2ζ44+2ζ52−2ζ68+2ζ76+2ζ92+2ζ1162ζ4+2ζ28+2ζ44−2ζ52+2ζ68−2ζ76−2ζ92−2ζ11601−2525-1-110000000000ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ1165−500000000000000000000000000000000
χ6888-8-8-4-4440-222-20002ζ4+2ζ28+2ζ44−2ζ52+2ζ68−2ζ76−2ζ92−2ζ116−2ζ4−2ζ28−2ζ44+2ζ52−2ζ68+2ζ76+2ζ92+2ζ116−2ζ4+2ζ28−2ζ44−2ζ52+2ζ68+2ζ76−2ζ92+2ζ1162ζ4−2ζ28+2ζ44+2ζ52−2ζ68−2ζ76+2ζ92−2ζ1160125−25-1-110000000000−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−5500000000000000000000000000000000
χ6988-8-8-4-4440-222-2000−2ζ4−2ζ28−2ζ44+2ζ52−2ζ68+2ζ76+2ζ92+2ζ1162ζ4+2ζ28+2ζ44−2ζ52+2ζ68−2ζ76−2ζ92−2ζ1162ζ4−2ζ28+2ζ44+2ζ52−2ζ68−2ζ76+2ζ92−2ζ116−2ζ4+2ζ28−2ζ44−2ζ52+2ζ68+2ζ76−2ζ92+2ζ1160125−25-1-110000000000ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−5500000000000000000000000000000000
χ708-88-88-88-80-2-22200000000-200-22200000−2525−2525000000000000000000000000000000000000000
χ718-88-88-88-80-2-22200000000-200-2220000025−2525−25000000000000000000000000000000000000000
χ728-8-888-8-880-22-2200000000-2002-2200000−252525−25000000000000000000000000000000000000000
χ738-8-888-8-880-22-2200000000-2002-220000025−25−2525000000000000000000000000000000000000000
χ7416-1616-16-88-880-4-444000000002002-2-2000000000000000000000000000000000000000000000000
χ7516-16-1616-888-80-44-4400000000200-22-2000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.