Finite Group Databasebeta

← Group #11752454

Character table — Group #11752454

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222222244444444444444444444558888888888888888881010101010101020202020202020206060606060606060
order122344612122456661012121215152020303060606060441010102020203030303030306060606060602246612122466612121244448888
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
χ5111111111-1-111-1-111-1-11111111111111-1-11-1-111-1-1-1-111-1-1-1-11111111-1-11-1-11-1-11111-1-1-1-1
χ6111111111-1-111-1-111-1-11111111111111-1-11-1-111-1-1-1-111-1-1-1-11111111-1-11-1-11-1-1-1-1-1-11111
χ7111111111-1-111-1-111-1-11111111111-1-11-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-111-111ii−i−i−i−iii
χ8111111111-1-111-1-111-1-11111111111-1-11-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-111-111−i−iiiii−i−i
χ911-111-11-1-11-11-11111-1-111-1-111-1-1-1-111-1111-1-1-1-1111111-1-1-1-1-11-1-1-111-111-1-1-1111-11-11-11-1
χ1011-111-11-1-11-11-11111-1-111-1-111-1-1-1-111-1111-1-1-1-1111111-1-1-1-1-11-1-1-111-111-1-1-111-11-11-11-11
χ1111-111-11-1-11-11-11111-1-111-1-111-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-11-1111-1-11-1-1111-1-1i−i−iii−i−ii
χ1211-111-11-1-11-11-11111-1-111-1-111-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-11-1111-1-11-1-1111-1-1−iii−i−iii−i
χ1311-111-11-1-1-111-1-1-1111111-1-111-1-1-1-111-1-1-1111-1-1-1-1-1-1111111-11-1-1-1111-1111-1-1-11-11-1-11-11
χ1411-111-11-1-1-111-1-1-1111111-1-111-1-1-1-111-1-1-1111-1-1-1-1-1-1111111-11-1-1-1111-1111-1-1-1-11-111-11-1
χ1511-111-11-1-1-111-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111111-1111-1-1-11-1-1-1111i−i−ii−iii−i
χ1611-111-11-1-1-111-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111111-1111-1-1-11-1-1-1111−iii−ii−i−ii
χ172222-2-22-2-20022002-20022-2-222-2-2-2-222200-200220000-2-20000-2-22-2-22200-20020000000000
χ182222-2-22-2-20022002-20022-2-222-2-2-2-2-2-2200-200220000-2-2000022-222-2-200200-20000000000
χ19222-122-1-1-1222-1-1-12-1-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-100000000
χ20222-122-1-1-1222-1-1-12-1-1-1-1-122-1-1-1-1-1-1-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111-2-211111100000000
χ21222-122-1-1-1-2-22-1112-111-1-122-1-1-1-1-1-1222-2-22-2-2-1-11111-1-11111222-1-1-1-1-2-2-111-11100000000
χ22222-122-1-1-1-2-22-1112-111-1-122-1-1-1-1-1-1-2-22-2-22-2-2-1-11111-1-11111-2-2-21111221-1-11-1-100000000
χ23222-1-2-2-111002-1−i3i321−i3i3-1-1-2-2-1-1111122200-200-1-1−i3−i3i3i311−i3−i3i3i3-2-2211-1-1001−i3i3-1−i3i300000000
χ24222-1-2-2-111002-1−i3i321−i3i3-1-1-2-2-1-11111-2-2200-200-1-1−i3−i3i3i311−i3−i3i3i322-2-1-11100-1i3−i31i3−i300000000
χ25222-1-2-2-111002-1i3−i321i3−i3-1-1-2-2-1-1111122200-200-1-1i3i3−i3−i311i3i3−i3−i3-2-2211-1-1001i3−i3-1i3−i300000000
χ26222-1-2-2-111002-1i3−i321i3−i3-1-1-2-2-1-11111-2-2200-200-1-1i3i3−i3−i311i3i3−i3−i322-2-1-11100-1−i3i31−i3i300000000
χ2722-22-22222002-2002-200222222222222-200-200-2-20000-2-200002-2-2222200-200-20000000000
χ2822-22-22222002-2002-2002222222222-2-2-200-200-2-20000-2-20000-222-2-2-2-20020020000000000
χ2922-2-12-2-1112-221-1-12-111-1-1-2-2-1-1111122-2222-2-211-1-1-1-1-1-11111-22-211-1-1-22-1111-1-100000000
χ3022-2-12-2-1112-221-1-12-111-1-1-2-2-1-11111-2-2-2222-2-211-1-1-1-1-1-111112-22-1-1112-21-1-1-11100000000
χ3122-2-12-2-111-2221112-1-1-1-1-1-2-2-1-1111122-2-2-2222111111-1-1-1-1-1-1-22-211-1-12-2-1-1-111100000000
χ3222-2-12-2-111-2221112-1-1-1-1-1-2-2-1-11111-2-2-2-2-2222111111-1-1-1-1-1-12-22-1-111-22111-1-1-100000000
χ3322-2-1-22-1-1-10021−i3i321i3−i3-1-122-1-1-1-1-1-122-200-20011−i3−i3i3i311i3i3−i3−i32-2-2-1-1-1-1001i3−i31−i3i300000000
χ3422-2-1-22-1-1-10021−i3i321i3−i3-1-122-1-1-1-1-1-1-2-2-200-20011−i3−i3i3i311i3i3−i3−i3-222111100-1−i3i3-1i3−i300000000
χ3522-2-1-22-1-1-10021i3−i321−i3i3-1-122-1-1-1-1-1-122-200-20011i3i3−i3−i311−i3−i3i3i32-2-2-1-1-1-1001−i3i31i3−i300000000
χ3622-2-1-22-1-1-10021i3−i321−i3i3-1-122-1-1-1-1-1-1-2-2-200-20011i3i3−i3−i311−i3−i3i3i3-222111100-1i3−i3-1−i3i300000000
χ3744444444444-1444-1444-1-1-1-1-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ38444444444-4-4-14-4-4-14-4-4-1-1-1-1-1-1-1-1-1-100-111-111-1-11111-1-1111100000000000000000000000
χ394444-4-44-4-400-1400-1-400-1-111-1-1111100-1−551−55-1-1−55−5511−55−5500000000000000000000000
χ404444-4-44-4-400-1400-1-400-1-111-1-1111100-15−515−5-1-15−55−5115−55−500000000000000000000000
χ41444-244-2-2-244-1-2-2-2-1-2-2-21−i1521+i152-1-11−i1521+i1521−i1521−i1521+i1521+i15200-1-1-1-1-1-11−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521+i1521−i15200000000000000000000000
χ42444-244-2-2-244-1-2-2-2-1-2-2-21+i1521−i152-1-11+i1521−i1521+i1521+i1521−i1521−i15200-1-1-1-1-1-11+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521−i1521+i15200000000000000000000000
χ43444-244-2-2-2-4-4-1-222-1-2221−i1521+i152-1-11−i1521+i1521−i1521−i1521+i1521+i15200-111-1111−i1521+i152−1+i152−1−i152−1−i152−1+i1521−i1521+i152−1+i152−1−i152−1−i152−1+i15200000000000000000000000
χ44444-244-2-2-2-4-4-1-222-1-2221+i1521−i152-1-11+i1521−i1521+i1521+i1521−i1521−i15200-111-1111+i1521−i152−1−i152−1+i152−1+i152−1−i1521+i1521−i152−1−i152−1+i152−1+i152−1−i15200000000000000000000000
χ45444-2-4-4-22200-1-2−2i32i3-12−2i32i31−i1521+i152111−i1521+i152−1+i152−1+i152−1−i152−1−i15200-15−515−51−i1521+i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−1+i152−1−i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ5800000000000000000000000
χ46444-2-4-4-22200-1-2−2i32i3-12−2i32i31+i1521−i152111+i1521−i152−1−i152−1−i152−1+i152−1+i15200-1−551−551+i1521−i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−1−i152−1+i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ4600000000000000000000000
χ47444-2-4-4-22200-1-22i3−2i3-122i3−2i31−i1521+i152111−i1521+i152−1+i152−1+i152−1−i152−1−i15200-1−551−551−i1521+i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ5800000000000000000000000
χ48444-2-4-4-22200-1-22i3−2i3-122i3−2i31+i1521−i152111+i1521−i152−1−i152−1−i152−1+i152−1+i15200-15−515−51+i1521−i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−1−i152−1+i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ4600000000000000000000000
χ4944-444-44-4-44-4-1-444-14-4-4-1-111-1-11111001-1-1-11111-1-1-1-1-1-1111100000000000000000000000
χ5044-444-44-4-4-44-1-4-4-4-1444-1-111-1-1111100111-1-1-1111111-1-1-1-1-1-100000000000000000000000
χ5144-44-4444400-1-400-1-400-1-1-1-1-1-1-1-1-1-1001−5515−511−55−55115−55−500000000000000000000000
χ5244-44-4444400-1-400-1-400-1-1-1-1-1-1-1-1-1-10015−51−55115−55−511−55−5500000000000000000000000
χ5344-4-24-4-2224-4-12-2-2-1-2221−i1521+i152111−i1521+i152−1+i152−1+i152−1−i152−1−i152001-1-1-111−1+i152−1−i1521−i1521+i1521+i1521−i1521−i1521+i152−1+i152−1−i152−1−i152−1+i15200000000000000000000000
χ5444-4-24-4-2224-4-12-2-2-1-2221+i1521−i152111+i1521−i152−1−i152−1−i152−1+i152−1+i152001-1-1-111−1−i152−1+i1521+i1521−i1521−i1521+i1521+i1521−i152−1−i152−1+i152−1+i152−1−i15200000000000000000000000
χ5544-4-24-4-222-44-1222-1-2-2-21−i1521+i152111−i1521+i152−1+i152−1+i152−1−i152−1−i15200111-1-1-1−1+i152−1−i152−1+i152−1−i152−1−i152−1+i1521−i1521+i1521−i1521+i1521+i1521−i15200000000000000000000000
χ5644-4-24-4-222-44-1222-1-2-2-21+i1521−i152111+i1521−i152−1−i152−1−i152−1+i152−1+i15200111-1-1-1−1−i152−1+i152−1−i152−1+i152−1+i152−1−i1521+i1521−i1521+i1521−i1521−i1521+i15200000000000000000000000
χ5744-4-2-44-2-2-200-12−2i32i3-122i3−2i31−i1521+i152-1-11−i1521+i1521−i1521−i1521+i1521+i1520015−51−55−1+i152−1−i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ5800000000000000000000000
χ5844-4-2-44-2-2-200-12−2i32i3-122i3−2i31+i1521−i152-1-11+i1521−i1521+i1521+i1521−i1521−i152001−5515−5−1−i152−1+i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−1−i152−1+i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ4600000000000000000000000
χ5944-4-2-44-2-2-200-122i3−2i3-12−2i32i31−i1521+i152-1-11−i1521+i1521−i1521−i1521+i1521+i152001−5515−5−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−1+i152−1−i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ5800000000000000000000000
χ6044-4-2-44-2-2-200-122i3−2i3-12−2i32i31+i1521−i152-1-11+i1521−i1521+i1521+i1521−i1521−i1520015−51−55−1−i152−1+i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−1−i152−1+i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ4600000000000000000000000
χ614-40400-400004000-40004400-4-400004i−4i000000000000000000000004i−4i0000000000000000
χ624-40400-400004000-40004400-4-40000−4i4i00000000000000000000000−4i4i0000000000000000
χ634-40-200223−23004000-4000-2-2002223−2323−234i−4i000000000000000000000−2i32i3−2i2i0000000000000000
χ644-40-200223−23004000-4000-2-2002223−2323−23−4i4i0000000000000000000002i3−2i32i−2i0000000000000000
χ654-40-2002−2323004000-4000-2-20022−2323−23234i−4i0000000000000000000002i3−2i3−2i2i0000000000000000
χ664-40-2002−2323004000-4000-2-20022−2323−2323−4i4i000000000000000000000−2i32i32i−2i0000000000000000
χ678-80800-80000-20002000-2-2−2i52i522−2i52i52i5−2i50000000000000000000000000000000000000000000
χ688-80800-80000-20002000-2-22i5−2i5222i5−2i5−2i52i50000000000000000000000000000000000000000000
χ698-80-400443−4300-200020001−i151+i152i5−2i5−1+i15−1−i152ζ7−2ζ11+2ζ43−2ζ59−2ζ7+2ζ11−2ζ43+2ζ592ζ19−2ζ23+2ζ31−2ζ47−2ζ19+2ζ23−2ζ31+2ζ470000000000000000000000000000000000000000000
χ708-80-400443−4300-200020001+i151−i15−2i52i5−1−i15−1+i152ζ19−2ζ23+2ζ31−2ζ47−2ζ19+2ζ23−2ζ31+2ζ472ζ7−2ζ11+2ζ43−2ζ59−2ζ7+2ζ11−2ζ43+2ζ590000000000000000000000000000000000000000000
χ718-80-4004−434300-200020001−i151+i15−2i52i5−1+i15−1−i15−2ζ7+2ζ11−2ζ43+2ζ592ζ7−2ζ11+2ζ43−2ζ59−2ζ19+2ζ23−2ζ31+2ζ472ζ19−2ζ23+2ζ31−2ζ470000000000000000000000000000000000000000000
χ728-80-4004−434300-200020001+i151−i152i5−2i5−1−i15−1+i15−2ζ19+2ζ23−2ζ31+2ζ472ζ19−2ζ23+2ζ31−2ζ47−2ζ7+2ζ11−2ζ43+2ζ592ζ7−2ζ11+2ζ43−2ζ590000000000000000000000000000000000000000000

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