Finite Group Databasebeta

← Group #11752443

Character table — Group #11752443

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222222244444444444444444444558888888888888888881010101010101020202020202020206060606060606060
order122344666445101010121212121212151530303030303044202020202020606060606060606060606060224121212122266666644448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ411111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ5111111111-1-1111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-1
χ6111111111-1-1111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111
χ7111111111-1-1111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−i−i−iii
χ8111111111-1-1111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iiiii−i−i
χ911-111-1-1-111-11-1-111-111-1-111-1-1-1-111111-111-1-111-1-11111-1-1-1-1-11-111-1-11-11-111-1-11-11-11-11-1
χ1011-111-1-1-111-11-1-111-111-1-111-1-1-1-111111-111-1-111-1-11111-1-1-1-1-11-111-1-11-11-111-1-1-11-11-11-11
χ1111-111-1-1-111-11-1-111-111-1-111-1-1-1-111-1-11-111-1-111-1-11111-1-1-1-11-11-1-111-11-11-1-111i−i−iii−i−ii
χ1211-111-1-1-111-11-1-111-111-1-111-1-1-1-111-1-11-111-1-111-1-11111-1-1-1-11-11-1-111-11-11-1-111−iii−i−iii−i
χ1311-111-1-1-11-111-1-111-1-1-11111-1-1-1-111111-1-1-11111-1-1-1-1-1-11111-11-111-1-1-111-1-1-1111-11-1-11-11
χ1411-111-1-1-11-111-1-111-1-1-11111-1-1-1-111111-1-1-11111-1-1-1-1-1-11111-11-111-1-1-111-1-1-111-11-111-11-1
χ1511-111-1-1-11-111-1-111-1-1-11111-1-1-1-111-1-11-1-1-11111-1-1-1-1-1-111111-11-1-1111-1-1111-1-1i−i−ii−iii−i
χ1611-111-1-1-11-111-1-111-1-1-11111-1-1-1-111-1-11-1-1-11111-1-1-1-1-1-111111-11-1-1111-1-1111-1-1−iii−ii−i−ii
χ172222-2-2222002222-2-200002222222222-2-20000-2-2-2-200000000-2-22222200-2-2000000000000
χ182222-2-2222002222-2-2000022222222-2-2-2-20000-2-2-2-20000000022-2-2-2-2-20022000000000000
χ19222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-100000000
χ20222-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111-2-211111100000000
χ21222-122-1-1-1-2-22222-1-11111-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111222-1-1-1-1-2-2-1-1111100000000
χ22222-122-1-1-1-2-22222-1-11111-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-1-1-111111111-2-2-211112211-1-1-1-100000000
χ23222-1-2-2-1-1-100222211−i3i3−i3i3-1-1-1-1-1-1-1-122-2-200001111−i3−i3i3i3−i3−i3i3i3-2-22-1-1-1-10011−i3i3−i3i300000000
χ24222-1-2-2-1-1-100222211−i3i3−i3i3-1-1-1-1-1-1-1-1-2-2-2-200001111−i3−i3i3i3−i3−i3i3i322-2111100-1-1i3−i3i3−i300000000
χ25222-1-2-2-1-1-100222211i3−i3i3−i3-1-1-1-1-1-1-1-122-2-200001111i3i3−i3−i3i3i3−i3−i3-2-22-1-1-1-10011i3−i3i3−i300000000
χ26222-1-2-2-1-1-100222211i3−i3i3−i3-1-1-1-1-1-1-1-1-2-2-2-200001111i3i3−i3−i3i3i3−i3−i322-2111100-1-1−i3i3−i3i300000000
χ2722-22-22-2-22002-2-22-22000022-2-2-2-22222-220000-2-222000000002-2-222-2-200-22000000000000
χ2822-22-22-2-22002-2-22-22000022-2-2-2-222-2-2-220000-2-22200000000-222-2-222002-2000000000000
χ2922-2-12-211-12-22-2-22-11-1-111-1-11111-1-1222-222-2-2-1-111-1-1-1-11111-22-2-1-1112-2-11-1-11100000000
χ3022-2-12-211-12-22-2-22-11-1-111-1-11111-1-1-2-22-222-2-2-1-111-1-1-1-111112-2211-1-1-221-111-1-100000000
χ3122-2-12-211-1-222-2-22-1111-1-1-1-11111-1-1222-2-2-222-1-1111111-1-1-1-1-22-2-1-111-22-1111-1-100000000
χ3222-2-12-211-1-222-2-22-1111-1-1-1-11111-1-1-2-22-2-2-222-1-1111111-1-1-1-12-2211-1-12-21-1-1-11100000000
χ3322-2-1-2211-1002-2-221-1−i3i3i3−i3-1-11111-1-122-22000011-1-1−i3−i3i3i3i3i3−i3−i32-2-2-1-111001-1−i3i3i3−i300000000
χ3422-2-1-2211-1002-2-221-1−i3i3i3−i3-1-11111-1-1-2-2-22000011-1-1−i3−i3i3i3i3i3−i3−i3-22211-1-100-11i3−i3−i3i300000000
χ3522-2-1-2211-1002-2-221-1i3−i3−i3i3-1-11111-1-122-22000011-1-1i3i3−i3−i3−i3−i3i3i32-2-2-1-111001-1i3−i3−i3i300000000
χ3622-2-1-2211-1002-2-221-1i3−i3−i3i3-1-11111-1-1-2-2-22000011-1-1i3i3−i3−i3−i3−i3i3i3-22211-1-100-11−i3i3i3−i300000000
χ3744444444444-1-1-1-1444444-1-1-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ38444444444-4-4-1-1-1-144-4-4-4-4-1-1-1-1-1-1-1-100-1-11111-1-1-1-11111111100000000000000000000000
χ394444-4-444400-1-1-1-1-4-40000-1-1-1-1-1-1-1-10011−55−551111−55−55−55−5500000000000000000000000
χ404444-4-444400-1-1-1-1-4-40000-1-1-1-1-1-1-1-100115−55−511115−55−55−55−500000000000000000000000
χ41444-244-2-2-244-1-1-1-1-2-2-2-2-2-21−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i15200-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i15200000000000000000000000
χ42444-244-2-2-244-1-1-1-1-2-2-2-2-2-21+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i15200-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i15200000000000000000000000
χ43444-244-2-2-2-4-4-1-1-1-1-2-222221−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i15200-1-111111−i1521+i1521−i1521+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i15200000000000000000000000
χ44444-244-2-2-2-4-4-1-1-1-1-2-222221+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i15200-1-111111+i1521−i1521+i1521−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i15200000000000000000000000
χ45444-2-4-4-2-2-200-1-1-1-122−2i32i3−2i32i31−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i15200115−55−5−1+i152−1−i152−1+i152−1−i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ5800000000000000000000000
χ46444-2-4-4-2-2-200-1-1-1-122−2i32i3−2i32i31+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1520011−55−55−1−i152−1+i152−1−i152−1+i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ4600000000000000000000000
χ47444-2-4-4-2-2-200-1-1-1-1222i3−2i32i3−2i31−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1520011−55−55−1+i152−1−i152−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ5800000000000000000000000
χ48444-2-4-4-2-2-200-1-1-1-1222i3−2i32i3−2i31+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i15200115−55−5−1−i152−1+i152−1−i152−1+i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ4600000000000000000000000
χ4944-444-4-4-444-4-111-14-444-4-4-1-11111-1-100-11-1-111-1-111-1-1-1-1111100000000000000000000000
χ5044-444-4-4-44-44-111-14-4-4-444-1-11111-1-100-1111-1-1-1-1111111-1-1-1-100000000000000000000000
χ5144-44-44-4-4400-111-1-440000-1-11111-1-1001-1−555−511-1-1−55−555−55−500000000000000000000000
χ5244-44-44-4-4400-111-1-440000-1-11111-1-1001-15−5−5511-1-15−55−5−55−5500000000000000000000000
χ5344-4-24-422-24-4-111-1-22-2-2221−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i15200-11-1-1111−i1521+i152−1+i152−1−i1521−i1521+i1521+i1521−i152−1+i152−1−i152−1−i152−1+i15200000000000000000000000
χ5444-4-24-422-24-4-111-1-22-2-2221+i1521−i152−1−i152−1−i152−1+i152−1+i1521+i1521−i15200-11-1-1111+i1521−i152−1−i152−1+i1521+i1521−i1521−i1521+i152−1−i152−1+i152−1+i152−1−i15200000000000000000000000
χ5544-4-24-422-2-44-111-1-2222-2-21−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i15200-1111-1-11−i1521+i152−1+i152−1−i152−1+i152−1−i152−1−i152−1+i1521−i1521+i1521+i1521−i15200000000000000000000000
χ5644-4-24-422-2-44-111-1-2222-2-21+i1521−i152−1−i152−1−i152−1+i152−1+i1521+i1521−i15200-1111-1-11+i1521−i152−1−i152−1+i152−1−i152−1+i152−1+i152−1−i1521+i1521−i1521−i1521+i15200000000000000000000000
χ5744-4-2-4422-200-111-12-2−2i32i32i3−2i31−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i152001-15−5−55−1+i152−1−i1521−i1521+i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ5800000000000000000000000
χ5844-4-2-4422-200-111-12-2−2i32i32i3−2i31+i1521−i152−1−i152−1−i152−1+i152−1+i1521+i1521−i152001-1−555−5−1−i152−1+i1521+i1521−i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ4600000000000000000000000
χ5944-4-2-4422-200-111-12-22i3−2i3−2i32i31−i1521+i152−1+i152−1+i152−1−i152−1−i1521−i1521+i152001-1−555−5−1+i152−1−i1521−i1521+i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ5800000000000000000000000
χ6044-4-2-4422-200-111-12-22i3−2i3−2i32i31+i1521−i152−1−i152−1−i152−1+i152−1+i1521+i1521−i152001-15−5−55−1−i152−1+i1521+i1521−i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ4600000000000000000000000
χ614-4040000-400400-4000000440000-4-44i−4i0000000000000000000004i−4i000000000000000000
χ624-4040000-400400-4000000440000-4-4−4i4i000000000000000000000−4i4i000000000000000000
χ634-40-200−2i32i3200400-4000000-2-2−2i32i3−2i32i3224i−4i000000000000000000000−2i2i23−230000000000000000
χ644-40-200−2i32i3200400-4000000-2-2−2i32i3−2i32i322−4i4i0000000000000000000002i−2i−23230000000000000000
χ654-40-2002i3−2i3200400-4000000-2-22i3−2i32i3−2i3224i−4i000000000000000000000−2i2i−23230000000000000000
χ664-40-2002i3−2i3200400-4000000-2-22i3−2i32i3−2i322−4i4i0000000000000000000002i−2i23−230000000000000000
χ678-8080000-800-2−25252000000-2-2−252525−25220000000000000000000000000000000000000000000
χ688-8080000-800-225−252000000-2-225−25−2525220000000000000000000000000000000000000000000
χ698-80-400−4i34i3400-2−252520000001+i151−i152ζ2−2ζ34+2ζ38−2ζ46−2ζ2+2ζ34−2ζ38+2ζ462ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ58−1−i15−1+i150000000000000000000000000000000000000000000
χ708-80-400−4i34i3400-225−2520000001−i151+i152ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ582ζ2−2ζ34+2ζ38−2ζ46−2ζ2+2ζ34−2ζ38+2ζ46−1+i15−1−i150000000000000000000000000000000000000000000
χ718-80-4004i3−4i3400-2−252520000001−i151+i15−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ58−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−1+i15−1−i150000000000000000000000000000000000000000000
χ728-80-4004i3−4i3400-225−2520000001+i151−i15−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ58−1−i15−1+i150000000000000000000000000000000000000000000

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