Finite Group Databasebeta

← Group #14514375

Character table — Group #14514375

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1124444556688881016161616161616162424303040404040606060606060606011244445566888810161616161616161624243030404040406060606060606060
order12251010102244366621515303030303030202044666644448888222101010102244666623030303030303030202044666644448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111-1-1111111-11111111111-1-1-1-1-1-1ii−i−iii−i−i1111111-1-1111111-11111111111-1-1-1-1-1-1ii−i−iii−i−i
χ41111111-1-1111111-11111111111-1-1-1-1-1-1−i−iii−i−iii1111111-1-1111111-11111111111-1-1-1-1-1-1−i−iii−i−iii
χ511-11-1-11111-111-1-1-11111-1-1-1-11-1-1111-1-11-11-11-11-111-11-1-11111-111-1-1-11111-1-1-1-11-1-1111-1-11-11-11-11-1
χ611-11-1-11111-111-1-1-11111-1-1-1-11-1-1111-1-1-11-11-11-1111-11-1-11111-111-1-1-11111-1-1-1-11-1-1111-1-1-11-11-11-11
χ711-11-1-11-1-11-111-1-111111-1-1-1-11-11-1-1-111i−i−iii−i−ii11-11-1-11-1-11-111-1-111111-1-1-1-11-11-1-1-111i−i−iii−i−ii
χ811-11-1-11-1-11-111-1-111111-1-1-1-11-11-1-1-111−iii−i−iii−i11-11-1-11-1-11-111-1-111111-1-1-1-11-11-1-1-111−iii−i−iii−i
χ922222222222-1-1-1-12-1-1-1-1-1-1-1-12222-1-1-1-10000000022222222222-1-1-1-12-1-1-1-1-1-1-1-12222-1-1-1-100000000
χ102222222-2-222-1-1-1-1-2-1-1-1-1-1-1-1-122-2-21111000000002222222-2-222-1-1-1-1-2-1-1-1-1-1-1-1-122-2-2111100000000
χ1122-22-2-22222-2-1-111-2-1-1-1-111112-2-22-1-1110000000022-22-2-22222-2-1-111-2-1-1-1-111112-2-22-1-11100000000
χ1222-22-2-22-2-22-2-1-1112-1-1-1-111112-22-211-1-10000000022-22-2-22-2-22-2-1-1112-1-1-1-111112-22-211-1-100000000
χ13333333333-1-10000300000000-1-1-1-100001111-1-1-1-1333333333-1-10000300000000-1-1-1-100001111-1-1-1-1
χ14333333333-1-10000300000000-1-1-1-10000-1-1-1-11111333333333-1-10000300000000-1-1-1-10000-1-1-1-11111
χ153333333-3-3-1-10000-300000000-1-1110000ii−i−i−i−iii3333333-3-3-1-10000-300000000-1-1110000ii−i−i−i−iii
χ163333333-3-3-1-10000-300000000-1-1110000−i−iiiii−i−i3333333-3-3-1-10000-300000000-1-1110000−i−iiiii−i−i
χ1733-33-3-3333-110000-300000000-111-100001-11-1-11-1133-33-3-3333-110000-300000000-111-100001-11-1-11-11
χ1833-33-3-3333-110000-300000000-111-10000-11-111-11-133-33-3-3333-110000-300000000-111-10000-11-111-11-1
χ1933-33-3-33-3-3-110000300000000-11-110000i−i−ii−iii−i33-33-3-33-3-3-110000300000000-11-110000i−i−ii−iii−i
χ2033-33-3-33-3-3-110000300000000-11-110000−iii−ii−i−ii33-33-3-33-3-3-110000300000000-11-110000−iii−ii−i−ii
χ21444-1-1-1-1004444440-1-1-1-1-1-1-1-1-1-100000000000000444-1-1-1-1004444440-1-1-1-1-1-1-1-1-1-100000000000000
χ22444-1-1-1-10044-2-2-2-201−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152-1-100000000000000444-1-1-1-10044-2-2-2-201−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152-1-100000000000000
χ23444-1-1-1-10044-2-2-2-201+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152-1-100000000000000444-1-1-1-10044-2-2-2-201+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152-1-100000000000000
χ2444-4-111-1004-444-4-40-1-1-1-11111-110000000000000044-4-111-1004-444-4-40-1-1-1-11111-1100000000000000
χ2544-4-111-1004-4-2-22201−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152-110000000000000044-4-111-1004-4-2-22201−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152-1100000000000000
χ2644-4-111-1004-4-2-22201+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152-110000000000000044-4-111-1004-4-2-22201+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152-1100000000000000
χ274-40400-44-4001-1−i3i3011-1-1−i3i3−i3i300001-1−i3i3000000004-40400-44-4001-1−i3i3011-1-1−i3i3−i3i300001-1−i3i300000000
χ284-40400-44-4001-1i3−i3011-1-1i3−i3i3−i300001-1i3−i3000000004-40400-44-4001-1i3−i3011-1-1i3−i3i3−i300001-1i3−i300000000
χ294-40400-44-400-22000-2-22200000000-2200000000004-40400-44-400-22000-2-22200000000-220000000000
χ304-40400-4-44001-1−i3i3011-1-1−i3i3−i3i30000-11i3−i3000000004-40400-4-44001-1−i3i3011-1-1−i3i3−i3i30000-11i3−i300000000
χ314-40400-4-44001-1i3−i3011-1-1i3−i3i3−i30000-11−i3i3000000004-40400-4-44001-1i3−i3011-1-1i3−i3i3−i30000-11−i3i300000000
χ324-40400-4-4400-22000-2-222000000002-200000000004-40400-4-4400-22000-2-222000000002-20000000000
χ338-80-2−2525200002-2−2i32i30−1−i152−1+i1521+i1521−i152ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ5800000000000000008-80-2−2525200002-2−2i32i30−1−i152−1+i1521+i1521−i152ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ580000000000000000
χ348-80-2−2525200002-22i3−2i30−1+i152−1−i1521−i1521+i152−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ4600000000000000008-80-2−2525200002-22i3−2i30−1+i152−1−i1521−i1521+i152−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ460000000000000000
χ358-80-2−252520000-4400011-1-1−555−500000000000000008-80-2−252520000-4400011-1-1−555−50000000000000000
χ368-80-225−25200002-2−2i32i30−1+i152−1−i1521−i1521+i152ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ4600000000000000008-80-225−25200002-2−2i32i30−1+i152−1−i1521−i1521+i152ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ460000000000000000
χ378-80-225−25200002-22i3−2i30−1−i152−1+i1521+i1521−i152−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ5800000000000000008-80-225−25200002-22i3−2i30−1−i152−1+i1521+i1521−i152−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ580000000000000000
χ388-80-225−2520000-4400011-1-15−5−5500000000000000008-80-225−2520000-4400011-1-15−5−550000000000000000
χ39121212-3-3-3-300-4-400000000000001100000000000000121212-3-3-3-300-4-400000000000001100000000000000
χ401212-12-333-300-4400000000000001-1000000000000001212-12-333-300-4400000000000001-100000000000000
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ431111111-1-1111111-11111111111-1-1-1-1-1-1ii−i−iii−i−i-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111−i−iii−i−iii
χ441111111-1-1111111-11111111111-1-1-1-1-1-1−i−iii−i−iii-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111ii−i−iii−i−i
χ4511-11-1-11111-111-1-1-11111-1-1-1-11-1-1111-1-11-11-11-11-1-1-11-111-1-1-1-11-1-1111-1-1-1-11111-111-1-1-111-11-11-11-11
χ4611-11-1-11111-111-1-1-11111-1-1-1-11-1-1111-1-1-11-11-11-11-1-11-111-1-1-1-11-1-1111-1-1-1-11111-111-1-1-1111-11-11-11-1
χ4711-11-1-11-1-11-111-1-111111-1-1-1-11-11-1-1-111i−i−iii−i−ii-1-11-111-111-11-1-111-1-1-1-1-11111-11-1111-1-1−iii−i−iii−i
χ4811-11-1-11-1-11-111-1-111111-1-1-1-11-11-1-1-111−iii−i−iii−i-1-11-111-111-11-1-111-1-1-1-1-11111-11-1111-1-1i−i−iii−i−ii
χ4922222222222-1-1-1-12-1-1-1-1-1-1-1-12222-1-1-1-100000000-2-2-2-2-2-2-2-2-2-2-21111-211111111-2-2-2-2111100000000
χ502222222-2-222-1-1-1-1-2-1-1-1-1-1-1-1-122-2-2111100000000-2-2-2-2-2-2-222-2-21111211111111-2-222-1-1-1-100000000
χ5122-22-2-22222-2-1-111-2-1-1-1-111112-2-22-1-11100000000-2-22-222-2-2-2-2211-1-121111-1-1-1-1-222-211-1-100000000
χ5222-22-2-22-2-22-2-1-1112-1-1-1-111112-22-211-1-100000000-2-22-222-222-2211-1-1-21111-1-1-1-1-22-22-1-11100000000
χ53333333333-1-10000300000000-1-1-1-100001111-1-1-1-1-3-3-3-3-3-3-3-3-3110000-30000000011110000-1-1-1-11111
χ54333333333-1-10000300000000-1-1-1-10000-1-1-1-11111-3-3-3-3-3-3-3-3-3110000-300000000111100001111-1-1-1-1
χ553333333-3-3-1-10000-300000000-1-1110000ii−i−i−i−iii-3-3-3-3-3-3-33311000030000000011-1-10000−i−iiiii−i−i
χ563333333-3-3-1-10000-300000000-1-1110000−i−iiiii−i−i-3-3-3-3-3-3-33311000030000000011-1-10000ii−i−i−i−iii
χ5733-33-3-3333-110000-300000000-111-100001-11-1-11-11-3-33-333-3-3-31-100003000000001-1-110000-11-111-11-1
χ5833-33-3-3333-110000-300000000-111-10000-11-111-11-1-3-33-333-3-3-31-100003000000001-1-1100001-11-1-11-11
χ5933-33-3-33-3-3-110000300000000-11-110000i−i−ii−iii−i-3-33-333-3331-10000-3000000001-11-10000−iii−ii−i−ii
χ6033-33-3-33-3-3-110000300000000-11-110000−iii−ii−i−ii-3-33-333-3331-10000-3000000001-11-10000i−i−ii−iii−i
χ61444-1-1-1-1004444440-1-1-1-1-1-1-1-1-1-100000000000000-4-4-4111100-4-4-4-4-4-40111111111100000000000000
χ62444-1-1-1-10044-2-2-2-201−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i152-1-100000000000000-4-4-4111100-4-422220−1+i152−1−i152−1+i152−1−i152−1+i152−1+i152−1−i152−1−i1521100000000000000
χ63444-1-1-1-10044-2-2-2-201+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i152-1-100000000000000-4-4-4111100-4-422220−1−i152−1+i152−1−i152−1+i152−1−i152−1−i152−1+i152−1+i1521100000000000000
χ6444-4-111-1004-444-4-40-1-1-1-11111-1100000000000000-4-441-1-1100-44-4-44401111-1-1-1-11-100000000000000
χ6544-4-111-1004-4-2-22201−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152-1100000000000000-4-441-1-1100-4422-2-20−1+i152−1−i152−1+i152−1−i1521−i1521−i1521+i1521+i1521-100000000000000
χ6644-4-111-1004-4-2-22201+i1521−i1521+i1521−i152−1−i152−1−i152−1+i152−1+i152-1100000000000000-4-441-1-1100-4422-2-20−1−i152−1+i152−1−i152−1+i1521+i1521+i1521−i1521−i1521-100000000000000
χ674-40400-44-4001-1−i3i3011-1-1−i3i3−i3i300001-1−i3i300000000-440-4004-4400-11i3−i30-1-111i3−i3i3−i30000-11i3−i300000000
χ684-40400-44-4001-1i3−i3011-1-1i3−i3i3−i300001-1i3−i300000000-440-4004-4400-11−i3i30-1-111−i3i3−i3i30000-11−i3i300000000
χ694-40400-44-400-22000-2-22200000000-220000000000-440-4004-44002-200022-2-2000000002-20000000000
χ704-40400-4-44001-1−i3i3011-1-1−i3i3−i3i30000-11i3−i300000000-440-40044-400-11i3−i30-1-111i3−i3i3−i300001-1−i3i300000000
χ714-40400-4-44001-1i3−i3011-1-1i3−i3i3−i30000-11−i3i300000000-440-40044-400-11−i3i30-1-111−i3i3−i3i300001-1i3−i300000000
χ724-40400-4-4400-22000-2-222000000002-20000000000-440-40044-4002-200022-2-200000000-220000000000
χ738-80-2−2525200002-2−2i32i30−1−i152−1+i1521+i1521−i152ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ580000000000000000-880225−25-20000-222i3−2i301+i1521−i152−1−i152−1+i152−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ580000000000000000
χ748-80-2−2525200002-22i3−2i30−1+i152−1−i1521−i1521+i152−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ460000000000000000-880225−25-20000-22−2i32i301−i1521+i152−1+i152−1−i152ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ460000000000000000
χ758-80-2−252520000-4400011-1-1−555−50000000000000000-880225−25-200004-4000-1-1115−5−550000000000000000
χ768-80-225−25200002-2−2i32i30−1+i152−1−i1521−i1521+i152ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ460000000000000000-8802−2525-20000-222i3−2i301−i1521+i152−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ460000000000000000
χ778-80-225−25200002-22i3−2i30−1−i152−1+i1521+i1521−i152−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ580000000000000000-8802−2525-20000-22−2i32i301+i1521−i152−1−i152−1+i152ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ580000000000000000
χ788-80-225−2520000-4400011-1-15−5−550000000000000000-8802−2525-200004-4000-1-111−555−50000000000000000
χ79121212-3-3-3-300-4-400000000000001100000000000000-12-12-12333300440000000000000-1-100000000000000
χ801212-12-333-300-4400000000000001-100000000000000-12-12123-3-33004-40000000000000-1100000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.