Finite Group Databasebeta

← Group #11756993

Character table — Group #11756993

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222222222244444444444444444455888888888888888888101010101010101010101020202020202030303030303030303030303030303030
order122223444461212566610121212151520203030606060604410101020202030303030303060606060606022224446612126661212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ41111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ51111-111-1-1-11-1-1111-111-1-111-1-111-1-1-1-11111-11-1-11111-1-111-1-1-1-11-1-1-111-1-1-1111-1-111-11111-1-1-1-11111-1-1-1-1
χ61111-111-1-1-11-1-1111-111-1-111-1-111-1-1-1-11111-11-1-11111-1-111-1-1-1-11-1-1-111-1-1-1111-1-111-1-1-1-1-11111-1-1-1-11111
χ71111-111-1-1-11-1-1111-111-1-111-1-111-1-1-1-1-1-111-11-1-11111-1-111-1-1-1-1-1111-1-1111-1-1-111-1-11iiii−i−i−i−i−i−i−i−iiiii
χ81111-111-1-1-11-1-1111-111-1-111-1-111-1-1-1-1-1-111-11-1-11111-1-111-1-1-1-1-1111-1-1111-1-1-111-1-11−i−i−i−iiiiiiiii−i−i−i−i
χ9111-111-11-1-11-1-111-111-11-111-1-111-1-1-1-1111-11-11-111-1-111-1-111-1-1-11-1-11-11-1-111-11-11-1111-1-111-1-111-1-111-1-1
χ10111-111-11-1-11-1-111-111-11-111-1-111-1-1-1-1111-11-11-111-1-111-1-111-1-1-11-1-11-11-1-111-11-11-11-1-111-1-111-1-111-1-111
χ11111-111-11-1-11-1-111-111-11-111-1-111-1-1-1-1-1-11-11-11-111-1-111-1-111-1-11-111-11-111-1-11-11-11-1ii−i−iii−i−i−i−iii−i−iii
χ12111-111-11-1-11-1-111-111-11-111-1-111-1-1-1-1-1-11-11-11-111-1-111-1-111-1-11-111-11-111-1-11-11-11-1−i−iii−i−iiiii−i−iii−i−i
χ13111-1-11-1-11111111-1-11-1-111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1111-1-11111-1-111-1-111-1-1-1-11111-1-1-1-111
χ14111-1-11-1-11111111-1-11-1-111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1
χ15111-1-11-1-11111111-1-11-1-111111111111-1-11-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ16111-1-11-1-11111111-1-11-1-111111111111-1-11-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-111-1-111−i−iiiii−i−iii−i−i−i−iii
χ1711-1111-1-11-11-1-11-1111-1-1111-1-111-1-1-1-111-111-1-11-1-11111-1-1-1-111-1-11-1-111-1-111-1-11-1111-11-11-11-11-11-11-11-1
χ1811-1111-1-11-11-1-11-1111-1-1111-1-111-1-1-1-111-111-1-11-1-11111-1-1-1-111-1-11-1-111-1-111-1-11-111-11-11-11-11-11-11-11-11
χ1911-1111-1-11-11-1-11-1111-1-1111-1-111-1-1-1-1-1-1-111-1-11-1-11111-1-1-1-11111-111-1-111-1-111-11-1-1i−ii−ii−ii−i−ii−ii−ii−ii
χ2011-1111-1-11-11-1-11-1111-1-1111-1-111-1-1-1-1-1-1-111-1-11-1-11111-1-1-1-11111-111-1-111-1-111-11-1-1−ii−ii−ii−iii−ii−ii−ii−i
χ2111-11-11-11-111111-11-11-11-1111111111111-11-1-11-1-1-111-1-1-1-111-1-1-11-11-11-11111-11-1-11-11-11-1-11-111-11-1-11-11
χ2211-11-11-11-111111-11-11-11-1111111111111-11-1-11-1-1-111-1-1-1-111-1-1-11-11-11-11111-11-1-11-1-11-111-11-1-11-111-11-1
χ2311-11-11-11-111111-11-11-11-11111111111-1-1-11-1-11-1-1-111-1-1-1-111-1-11-11-11-11-1-1-1-11-111-11i−ii−i−ii−ii−ii−iii−ii−i
χ2411-11-11-11-111111-11-11-11-11111111111-1-1-11-1-11-1-1-111-1-1-1-111-1-11-11-11-11-1-1-1-11-111-11−ii−iii−ii−ii−ii−i−ii−ii
χ2511-1-1111-1-111111-1-1111-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-11-1-11-1-1111111-1-1-1-111-1-111-1-111-1-111-1-11
χ2611-1-1111-1-111111-1-1111-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-11-1-11-1-1111111-1-1-1-11-111-1-111-1-111-1-111-1
χ2711-1-1111-1-111111-1-1111-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111-111-1-1-1-1-1-11111-1i−i−iii−i−ii−iii−i−iii−i
χ2811-1-1111-1-111111-1-1111-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111-111-1-1-1-1-1-11111-1−iii−i−iii−ii−i−iii−i−ii
χ2911-1-1-11111-11-1-11-1-1-1111111-1-111-1-1-1-111-1-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-111111-1-1-11-1-11-111-11-1-11-111-1
χ3011-1-1-11111-11-1-11-1-1-1111111-1-111-1-1-1-111-1-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-111111-1-1-1-111-11-1-11-111-11-1-11
χ3111-1-1-11111-11-1-11-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1111111-1-1-1-1-1111i−i−ii−iii−i−iii−ii−i−ii
χ3211-1-1-11111-11-1-11-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1111111-1-1-1-1-1111−iii−ii−i−iii−i−ii−iii−i
χ3322222-12222-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-10000000000000000
χ3422222-12222-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-1-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-211111111110000000000000000
χ352222-2-12-2-2-2-1112-1-112-111-1-1-2-2-1-111112222-22-2-2-1-1-1-111-1-111112-2-2-222-211-1-1-111-1-110000000000000000
χ362222-2-12-2-2-2-1112-1-112-111-1-1-2-2-1-11111-2-222-22-2-2-1-1-1-111-1-11111-2222-2-22-1-1111-1-111-10000000000000000
χ37222-22-1-22-2-2-1112-11-121-11-1-1-2-2-1-11111222-22-22-2-1-111-1-111-1-111-22-2-22-2211-1-11-11-11-10000000000000000
χ38222-22-1-22-2-2-1112-11-121-11-1-1-2-2-1-11111-2-22-22-22-2-1-111-1-111-1-1112-222-22-2-1-111-11-11-110000000000000000
χ39222-2-2-1-2-222-1-1-12-111211-1-1-122-1-1-1-1-1-1222-2-2-2-22-1-111111111-1-1-2-2222-2-2-1-1-1-111-1-1110000000000000000
χ40222-2-2-1-2-222-1-1-12-111211-1-1-122-1-1-1-1-1-1-2-22-2-2-2-22-1-111111111-1-122-2-2-2221111-1-111-1-10000000000000000
χ4122-222-1-2-22-2-11121-1-1211-1-1-1-2-2-1-1111122-222-2-2211-1-1-1-11111-1-1-2-22-2-22211-1-111-11-1-10000000000000000
χ4222-222-1-2-22-2-11121-1-1211-1-1-1-2-2-1-11111-2-2-222-2-2211-1-1-1-11111-1-122-222-2-2-1-111-1-11-1110000000000000000
χ4322-22-2-1-22-22-1-1-121-1121-11-1-122-1-1-1-1-1-122-22-2-22-211-1-11111-1-111-22-22-22-2-1-1-1-11-111-110000000000000000
χ4422-22-2-1-22-22-1-1-121-1121-11-1-122-1-1-1-1-1-1-2-2-22-2-22-211-1-11111-1-1112-22-22-221111-11-1-11-10000000000000000
χ4522-2-22-12-2-22-1-1-1211-12-111-1-122-1-1-1-1-1-122-2-222-2-21111-1-1-1-111112-2-22-2-22-1-1-1-1-11111-10000000000000000
χ4622-2-22-12-2-22-1-1-1211-12-111-1-122-1-1-1-1-1-1-2-2-2-222-2-21111-1-1-1-11111-222-222-211111-1-1-1-110000000000000000
χ4722-2-2-2-1222-2-11121112-1-1-1-1-1-2-2-1-1111122-2-2-2222111111-1-1-1-1-1-1222-2-2-2-211-1-1-1-1-11110000000000000000
χ4822-2-2-2-1222-2-11121112-1-1-1-1-1-2-2-1-11111-2-2-2-2-2222111111-1-1-1-1-1-1-2-2-22222-1-111111-1-1-10000000000000000
χ494444444444444-1444-1444-1-1-1-1-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000
χ5044444-24444-2-2-2-1-2-2-2-1-2-2-21−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+i152000000000000000000000000000000000
χ5144444-24444-2-2-2-1-2-2-2-1-2-2-21+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−i152000000000000000000000000000000000
χ524444-444-4-4-44-4-4-144-4-14-4-4-1-111-1-1111100-1-11-111-1-1-1-111-1-11111000000000000000000000000000000000
χ534444-4-24-4-4-4-222-1-2-22-1-2221−i1521+i152111−i1521+i152−1+i152−1+i152−1−i152−1−i15200-1-11-1111−i1521+i1521−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000000000000
χ544444-4-24-4-4-4-222-1-2-22-1-2221+i1521−i152111+i1521−i152−1−i152−1−i152−1+i152−1+i15200-1-11-1111+i1521−i1521+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000000000000
χ55444-444-44-4-44-4-4-14-44-1-44-4-1-111-1-1111100-11-11-11-1-111-1-111-1-111000000000000000000000000000000000
χ56444-44-2-44-4-4-222-1-22-2-12-221−i1521+i152111−i1521+i152−1+i152−1+i152−1−i152−1−i15200-11-11-111−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i152000000000000000000000000000000000
χ57444-44-2-44-4-4-222-1-22-2-12-221+i1521−i152111+i1521−i152−1−i152−1−i152−1+i152−1+i15200-11-11-111+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i152000000000000000000000000000000000
χ58444-4-44-4-444444-14-4-4-1-4-44-1-1-1-1-1-1-1-1-1-100-11111-1-1-111111111-1-1000000000000000000000000000000000
χ59444-4-4-2-4-444-2-2-2-1-222-122-21−i1521+i152-1-11−i1521+i1521−i1521−i1521+i1521+i15200-11111-11−i1521+i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152000000000000000000000000000000000
χ60444-4-4-2-4-444-2-2-2-1-222-122-21+i1521−i152-1-11+i1521−i1521+i1521+i1521−i1521−i15200-11111-11+i1521−i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152000000000000000000000000000000000
χ6144-4444-4-44-44-4-4-1-444-1-4-44-1-111-1-11111001-1-111-111-1-1-1-11111-1-1000000000000000000000000000000000
χ6244-444-2-4-44-4-222-12-2-2-122-21−i1521+i152111−i1521+i152−1+i152−1+i152−1−i152−1−i152001-1-111-1−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152000000000000000000000000000000000
χ6344-444-2-4-44-4-222-12-2-2-122-21+i1521−i152111+i1521−i152−1−i152−1−i152−1+i152−1+i152001-1-111-1−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152000000000000000000000000000000000
χ6444-44-44-44-44444-1-44-4-1-44-4-1-1-1-1-1-1-1-1-1-1001-111-1111-1-11111-1-111000000000000000000000000000000000
χ6544-44-4-2-44-44-2-2-2-12-22-12-221−i1521+i152-1-11−i1521+i1521−i1521−i1521+i1521+i152001-111-11−1+i152−1−i1521−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152−1+i152−1−i152000000000000000000000000000000000
χ6644-44-4-2-44-44-2-2-2-12-22-12-221+i1521−i152-1-11+i1521−i1521+i1521+i1521−i1521−i152001-111-11−1−i152−1+i1521+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152−1−i152−1+i152000000000000000000000000000000000
χ6744-4-4444-4-44444-1-4-44-14-4-4-1-1-1-1-1-1-1-1-1-10011-1-1111111-1-1-1-11111000000000000000000000000000000000
χ6844-4-44-24-4-44-2-2-2-122-2-1-2221−i1521+i152-1-11−i1521+i1521−i1521−i1521+i1521+i1520011-1-111−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000000000000
χ6944-4-44-24-4-44-2-2-2-122-2-1-2221+i1521−i152-1-11+i1521−i1521+i1521+i1521−i1521−i1520011-1-111−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000000000000
χ7044-4-4-44444-44-4-4-1-4-4-4-1444-1-111-1-1111100111-1-1-1111111-1-1-1-1-1-1000000000000000000000000000000000
χ7144-4-4-4-2444-4-222-1222-1-2-2-21−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+i152000000000000000000000000000000000
χ7244-4-4-4-2444-4-222-1222-1-2-2-21+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−i152000000000000000000000000000000000
χ734-400040000-4004000-40004400-4-400004i−4i0000000000000000000000000004i−4i0000000000000000000000
χ744-400040000-4004000-40004400-4-40000−4i4i000000000000000000000000000−4i4i0000000000000000000000
χ754-4000-20000223−234000-4000-2-2002223−2323−234i−4i0000000000000000000000000−2i32i3−2i2i0000000000000000000000
χ764-4000-20000223−234000-4000-2-2002223−2323−23−4i4i00000000000000000000000002i3−2i32i−2i0000000000000000000000
χ774-4000-200002−23234000-4000-2-20022−2323−23234i−4i00000000000000000000000002i3−2i3−2i2i0000000000000000000000
χ784-4000-200002−23234000-4000-2-20022−2323−2323−4i4i0000000000000000000000000−2i32i32i−2i0000000000000000000000
χ798-800080000-800-20002000-2-2−2i52i522−2i52i52i5−2i500000000000000000000000000000000000000000000000000000
χ808-800080000-800-20002000-2-22i5−2i5222i5−2i5−2i52i500000000000000000000000000000000000000000000000000000
χ818-8000-40000443−43-200020001−i151+i152i5−2i5−1+i15−1−i152ζ7−2ζ11+2ζ43−2ζ59−2ζ7+2ζ11−2ζ43+2ζ592ζ19−2ζ23+2ζ31−2ζ47−2ζ19+2ζ23−2ζ31+2ζ4700000000000000000000000000000000000000000000000000000
χ828-8000-40000443−43-200020001+i151−i15−2i52i5−1−i15−1+i152ζ19−2ζ23+2ζ31−2ζ47−2ζ19+2ζ23−2ζ31+2ζ472ζ7−2ζ11+2ζ43−2ζ59−2ζ7+2ζ11−2ζ43+2ζ5900000000000000000000000000000000000000000000000000000
χ838-8000-400004−4343-200020001−i151+i15−2i52i5−1+i15−1−i15−2ζ7+2ζ11−2ζ43+2ζ592ζ7−2ζ11+2ζ43−2ζ59−2ζ19+2ζ23−2ζ31+2ζ472ζ19−2ζ23+2ζ31−2ζ4700000000000000000000000000000000000000000000000000000
χ848-8000-400004−4343-200020001+i151−i152i5−2i5−1−i15−1+i15−2ζ19+2ζ23−2ζ31+2ζ472ζ19−2ζ23+2ζ31−2ζ47−2ζ7+2ζ11−2ζ43+2ζ592ζ7−2ζ11+2ζ43−2ζ5900000000000000000000000000000000000000000000000000000

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