Finite Group Databasebeta

← Group #14285326

Character table — Group #14285326

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222444448888888810101010121216161616161616161620202020242424242430304040404040404040404040404048486080120120120120120
order122236664510101021215202030303044442461010303030306060121212124101020204428888242424242424242420204648888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1
χ31111111111111111111111111-1-11111111111111-1-1-1-1-1-1-11111111111111-1-1-11-1-1-1-1-1
χ41111111111111111111111111-1-11111111111111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-111111-1-1-1i−ii−iiiii−i−i−i−i11-1-1-1i−ii−i
χ6111111111111111111111-1-1-1-111111111111-1-1-1-111111-1-1-1−ii−ii−i−i−i−iiiii11-1-1-1−ii−ii
χ7111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1i−ii−iiiii−i−i−i−i-1-11-11−ii−ii
χ8111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1−ii−ii−i−i−i−iiiii-1-11-11i−ii−i
χ91111111111111-11111111111111-1-1-1-1-1-1-1111111-1111111-111-1-111-1-111-1-1-1-11-1-111-1-1
χ101111111111111-11111111111111-1-1-1-1-1-1-1111111-1111111-1-1-111-1-111-1-111-1-11-1-1-1-111
χ111111111111111-111111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11-1-111
χ121111111111111-111111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1111-1-1
χ131111111111111-11111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-11111-1-11i−i−iiii−i−i−i−iii-1-1-111i−i−ii
χ141111111111111-11111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-11111-1-11−iii−i−i−iiiii−i−i-1-1-111−iii−i
χ151111111111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1111i−i−iiii−i−i−i−iii1111-1−iii−i
χ161111111111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1111−iii−i−i−iiiii−i−i1111-1i−i−ii
χ1722222222-222220-22-2-22222-2-222-20000000-2-22-22-2022-2-2-2-20000000000000002000000
χ1822222222-222220-22-2-22222-2-22-220000000-2-22-22-20-2-22222000000000000000-2000000
χ1922222222-222220-22-2-2222-222-22-20000000-2-2-22-22022-2-222000000000000000-2000000
χ2022222222-222220-22-2-2222-222-2-220000000-2-2-22-220-2-222-2-20000000000000002000000
χ212222-1-1-1-1222222-1-122-1-1-1222200-122-1-1-1-1-1-1-1-1-1-1000000022222-1-1-1-1-1-1-1-1000-100000
χ222222-1-1-1-1222222-1-122-1-1-1222200-122-1-1-1-1-1-1-1-1-1-100000002-2-2-2-211111111000-100000
χ232222-1-1-1-1222222-1-122-1-1-1-2-2-2-200-122-1-1-1-1-1-111110000000-22i−2i2i−2i−i−i−i−iiiii000100000
χ242222-1-1-1-1222222-1-122-1-1-1-2-2-2-200-122-1-1-1-1-1-111110000000-2−2i2i−2i2iiiii−i−i−i−i000100000
χ252222-1-1-1-122222-2-1-122-1-1-12222001-2-21111-1-1-1-1-1-10000000-222-2-2-1-111-1-111000100000
χ262222-1-1-1-122222-2-1-122-1-1-12222001-2-21111-1-1-1-1-1-10000000-2-2-22211-1-111-1-1000100000
χ272222-1-1-1-122222-2-1-122-1-1-1-2-2-2-2001-2-21111-1-11111000000022i−2i−2i2i−i−iiiii−i−i000-100000
χ282222-1-1-1-122222-2-1-122-1-1-1-2-2-2-2001-2-21111-1-1111100000002−2i2i2i−2iii−i−i−i−iii000-100000
χ29444444444-1-1-1-144-1-1-1-1-1-10000444-1-1-1-1-1-1-1-100004-1-1-1-1000000000000000-1-10000000
χ30444444444-1-1-1-144-1-1-1-1-1-10000-4-44-1-1-1-1-1-1-1-10000-41111000000000000000110000000
χ31444444444-1-1-1-1-44-1-1-1-1-1-1000044-4111111-1-10000-4-1-1-1-1000000000000000110000000
χ32444444444-1-1-1-1-44-1-1-1-1-1-10000-4-4-4111111-1-1000041111000000000000000-1-10000000
χ3344444444-4-1-1-1-10-4-111-1-1-100004-40−55−5−5551100000-1-111000000000000000−550000000
χ3444444444-4-1-1-1-10-4-111-1-1-100004-405−555−5−51100000-1-1110000000000000005−50000000
χ3544444444-4-1-1-1-10-4-111-1-1-10000-440−55−5−555110000011-1-10000000000000005−50000000
χ3644444444-4-1-1-1-10-4-111-1-1-10000-4405−555−5−5110000011-1-1000000000000000−550000000
χ374444-2-2-2-2-4444402-2-4-4-2-2-24-4-4400000000022-22-2200000000000000000000000000000
χ384444-2-2-2-2-4444402-2-4-4-2-2-2-444-4000000000222-22-200000000000000000000000000000
χ3944-4-444-4-404-44-400400-4-440000000000000000000000004i−4i0000000000000000000000
χ4044-4-444-4-404-44-400400-4-44000000000000000000000000−4i4i0000000000000000000000
χ414-44-44-44-4044-4-4004004-4-4400-40000000000040-4000000000000000000000000000000
χ424-44-44-44-4044-4-4004004-4-4-400400000000000-404000000000000000000000000000000
χ434-44-4-22-22044-4-400-200-222400-400000000000-20200000000000006−6006−600000000000
χ444-44-4-22-22044-4-400-200-222400-400000000000-2020000000000000−6600−6600000000000
χ454-44-4-22-22044-4-400-200-222-40040000000000020-20000000000000−i6i600i6−i600000000000
χ464-44-4-22-22044-4-400-200-222-40040000000000020-20000000000000i6−i600−i6i600000000000
χ474-4-444-4-4404-4-4400400-44-404-40000000000000-40400000000000000000000000000000
χ484-4-444-4-4404-4-4400400-44-40-44000000000000040-400000000000000000000000000000
χ494-4-44-222-204-4-4400-2002-2204-4000000000000020-200000000000000−i6i600−i6i6000000000
χ504-4-44-222-204-4-4400-2002-2204-4000000000000020-200000000000000i6−i600i6−i6000000000
χ514-4-44-222-204-4-4400-2002-220-440000000000000-202000000000000006−600−66000000000
χ524-4-44-222-204-4-4400-2002-220-440000000000000-20200000000000000−66006−6000000000
χ538888-4-4-4-48-2-2-2-28-41-2-2111000000-4-2-2111111000000000000000000000000000000000
χ548888-4-4-4-48-2-2-2-2-8-41-2-2111000000422-1-1-1-111000000000000000000000000000000000
χ558888-4-4-4-4-8-2-2-2-2041221110000000−252555−5−5-1-1000000000000000000000000000000000
χ568888-4-4-4-4-8-2-2-2-204122111000000025−25−5−555-1-1000000000000000000000000000000000
χ5788-8-888-8-80-22-2200-2−252522-20000000000000−2525000000000000000000000000000000000
χ5888-8-888-8-80-22-2200-225−2522-2000000000000025−25000000000000000000000000000000000
χ5988-8-8-4-44408-88-800-40044-4000000000000000000000000000000000000000000000000
χ6088-8-8-4-4440-22-22001−2525-1-11000000000ζ4+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+ζ1165−5000000000000000000000000000000000
χ6188-8-8-4-4440-22-22001−2525-1-11000000000−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−ζ1165−5000000000000000000000000000000000
χ6288-8-8-4-4440-22-2200125−25-1-11000000000−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+ζ116−55000000000000000000000000000000000
χ6388-8-8-4-4440-22-2200125−25-1-11000000000ζ4−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−ζ116−55000000000000000000000000000000000
χ648-88-88-88-80-2-22200-200-2220000000000000000000000−2i52i5000000000000000000000000
χ658-88-88-88-80-2-22200-200-22200000000000000000000002i5−2i5000000000000000000000000
χ668-8-888-8-880-222-200-2002-2200000000000000000000−252500000000000000000000000000
χ678-8-888-8-880-222-200-2002-220000000000000000000025−2500000000000000000000000000
χ6816-1616-16-88-880-4-444002002-2-2000000000000000000000000000000000000000000000000
χ6916-16-1616-888-80-444-400200-22-2000000000000000000000000000000000000000000000000

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