Finite Group Databasebeta

← Group #64074

Character table — Group #64074

Order 288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size112222222444444441212121211222222244444444121212121122222224444444412121212
order12234461212246661212124488366312126121261266612121212122424366312126121261266612121212122424
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111-1-1-1-111111111111111111-1-1-1-111111111111111111-1-1-1-1
χ3111111111-1-11-1-11-1-111-1-1111111111-1-11-1-11-1-111-1-1111111111-1-11-1-11-1-111-1-1
χ4111111111-1-11-1-11-1-1-1-111111111111-1-11-1-11-1-1-1-111111111111-1-11-1-11-1-1-1-111
χ511-11-111-1-11-1-1111-1-11-11-111-11-111-1-11-1-1111-1-11-11-111-11-111-1-11-1-1111-1-11-11-1
χ611-11-111-1-11-1-1111-1-1-11-1111-11-111-1-11-1-1111-1-1-11-1111-11-111-1-11-1-1111-1-1-11-11
χ711-11-111-1-1-11-1-1-11111-1-1111-11-111-1-1-11-1-1-11111-1-1111-11-111-1-1-11-1-1-11111-1-11
χ811-11-111-1-1-11-1-1-1111-111-111-11-111-1-1-11-1-1-1111-111-111-11-111-1-1-11-1-1-1111-111-1
χ92222-2-22-2-200200-20000002222-2-22-2-200200-20000002222-2-22-2-200200-2000000
χ10222-122-1-1-122-1-1-1-1-1-10000222-122-1-1-122-1-1-1-1-1-10000222-122-1-1-122-1-1-1-1-1-10000
χ11222-122-1-1-1-2-2-111-1110000222-122-1-1-1-2-2-111-1110000222-122-1-1-1-2-2-111-1110000
χ12222-1-2-2-11100-1−i3i31−i3i30000222-1-2-2-11100-1−i3i31−i3i30000222-1-2-2-11100-1−i3i31−i3i30000
χ13222-1-2-2-11100-1i3−i31i3−i30000222-1-2-2-11100-1i3−i31i3−i30000222-1-2-2-11100-1i3−i31i3−i30000
χ1422-222-222200-200-200000022-222-222200-200-200000022-222-222200-200-2000000
χ1522-2-12-2-1-1-1001−i3i31i3−i3000022-2-12-2-1-1-1001−i3i31i3−i3000022-2-12-2-1-1-1001−i3i31i3−i30000
χ1622-2-12-2-1-1-1001i3−i31−i3i3000022-2-12-2-1-1-1001i3−i31−i3i3000022-2-12-2-1-1-1001i3−i31−i3i30000
χ1722-2-1-22-1112-21-1-1-111000022-2-1-22-1112-21-1-1-111000022-2-1-22-1112-21-1-1-1110000
χ1822-2-1-22-111-22111-1-1-1000022-2-1-22-111-22111-1-1-1000022-2-1-22-111-22111-1-1-10000
χ194-40400-4000000000000004-40400-4000000000000004-40400-400000000000000
χ204-40-200223−230000000000004-40-200223−230000000000004-40-200223−23000000000000
χ214-40-2002−23230000000000004-40-2002−23230000000000004-40-2002−2323000000000000
χ22111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ2311111111111111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ24111111111-1-11-1-11-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ25111111111-1-11-1-11-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ2611-11-111-1-11-1-1111-1-11-11-1−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32
χ2711-11-111-1-11-1-1111-1-1-11-11−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i32
χ2811-11-111-1-1-11-1-1-11111-1-11−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32
χ2911-11-111-1-1-11-1-1-1111-111-1−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32
χ302222-2-22-2-200200-2000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i300−1+i3001−i3000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i300−1−i3001+i3000000
χ31222-122-1-1-122-1-1-1-1-1-10000−1+i3−1+i3−1+i31−i32−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i320000−1−i3−1−i3−1−i31+i32−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i320000
χ32222-122-1-1-1-2-2-111-1110000−1+i3−1+i3−1+i31−i32−1+i3−1+i31−i321−i321−i321−i31−i31−i32−1+i32−1+i321−i32−1+i32−1+i320000−1−i3−1−i3−1−i31+i32−1−i3−1−i31+i321+i321+i321+i31+i31+i32−1−i32−1−i321+i32−1−i32−1−i320000
χ33222-1-2-2-11100-1−i3i31−i3i30000−1+i3−1+i3−1+i31−i321−i31−i31−i32−1+i32−1+i32001−i323+i32−3−i32−1+i323+i32−3−i320000−1−i3−1−i3−1−i31+i321+i31+i31+i32−1−i32−1−i32001+i32−3+i323−i32−1−i32−3+i323−i320000
χ34222-1-2-2-11100-1i3−i31i3−i30000−1+i3−1+i3−1+i31−i321−i31−i31−i32−1+i32−1+i32001−i32−3−i323+i32−1+i32−3−i323+i320000−1−i3−1−i3−1−i31+i321+i31+i31+i32−1−i32−1−i32001+i323−i32−3+i32−1−i323−i32−3+i320000
χ3522-222-222200-200-2000000−1+i3−1+i31−i3−1+i3−1+i31−i3−1+i3−1+i3−1+i3001−i3001−i3000000−1−i3−1−i31+i3−1−i3−1−i31+i3−1−i3−1−i3−1−i3001+i3001+i3000000
χ3622-2-12-2-1-1-1001−i3i31i3−i30000−1+i3−1+i31−i31−i32−1+i31−i31−i321−i321−i3200−1+i323+i32−3−i32−1+i32−3−i323+i320000−1−i3−1−i31+i31+i32−1−i31+i31+i321+i321+i3200−1−i32−3+i323−i32−1−i323−i32−3+i320000
χ3722-2-12-2-1-1-1001i3−i31−i3i30000−1+i3−1+i31−i31−i32−1+i31−i31−i321−i321−i3200−1+i32−3−i323+i32−1+i323+i32−3−i320000−1−i3−1−i31+i31+i32−1−i31+i31+i321+i321+i3200−1−i323−i32−3+i32−1−i32−3+i323−i320000
χ3822-2-1-22-1112-21-1-1-1110000−1+i3−1+i31−i31−i321−i3−1+i31−i32−1+i32−1+i32−1+i31−i3−1+i321−i321−i321−i32−1+i32−1+i320000−1−i3−1−i31+i31+i321+i3−1−i31+i32−1−i32−1−i32−1−i31+i3−1−i321+i321+i321+i32−1−i32−1−i320000
χ3922-2-1-22-111-22111-1-1-10000−1+i3−1+i31−i31−i321−i3−1+i31−i32−1+i32−1+i321−i3−1+i3−1+i32−1+i32−1+i321−i321−i321−i320000−1−i3−1−i31+i31+i321+i3−1−i31+i32−1−i32−1−i321+i3−1−i3−1−i32−1−i32−1−i321+i321+i321+i320000
χ404-40400-400000000000000−2+2i32−2i30−2+2i3002−2i300000000000000−2−2i32+2i30−2−2i3002+2i300000000000000
χ414-40-200223−23000000000000−2+2i32−2i301−i300−1+i3−2ζ7−4ζ112ζ7+4ζ11000000000000−2−2i32+2i301+i300−1−i34ζ7+2ζ11−4ζ7−2ζ11000000000000
χ424-40-2002−2323000000000000−2+2i32−2i301−i300−1+i32ζ7+4ζ11−2ζ7−4ζ11000000000000−2−2i32+2i301+i300−1−i3−4ζ7−2ζ114ζ7+2ζ11000000000000
χ43111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ4411111111111111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ45111111111-1-11-1-11-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ46111111111-1-11-1-11-1-1-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ4711-11-111-1-11-1-1111-1-11-11-1−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32
χ4811-11-111-1-11-1-1111-1-1-11-11−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i32
χ4911-11-111-1-1-11-1-1-11111-1-11−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32
χ5011-11-111-1-1-11-1-1-1111-111-1−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32
χ512222-2-22-2-200200-2000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i300−1−i3001+i3000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i300−1+i3001−i3000000
χ52222-122-1-1-122-1-1-1-1-1-10000−1−i3−1−i3−1−i31+i32−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i320000−1+i3−1+i3−1+i31−i32−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i320000
χ53222-122-1-1-1-2-2-111-1110000−1−i3−1−i3−1−i31+i32−1−i3−1−i31+i321+i321+i321+i31+i31+i32−1−i32−1−i321+i32−1−i32−1−i320000−1+i3−1+i3−1+i31−i32−1+i3−1+i31−i321−i321−i321−i31−i31−i32−1+i32−1+i321−i32−1+i32−1+i320000
χ54222-1-2-2-11100-1−i3i31−i3i30000−1−i3−1−i3−1−i31+i321+i31+i31+i32−1−i32−1−i32001+i32−3+i323−i32−1−i32−3+i323−i320000−1+i3−1+i3−1+i31−i321−i31−i31−i32−1+i32−1+i32001−i323+i32−3−i32−1+i323+i32−3−i320000
χ55222-1-2-2-11100-1i3−i31i3−i30000−1−i3−1−i3−1−i31+i321+i31+i31+i32−1−i32−1−i32001+i323−i32−3+i32−1−i323−i32−3+i320000−1+i3−1+i3−1+i31−i321−i31−i31−i32−1+i32−1+i32001−i32−3−i323+i32−1+i32−3−i323+i320000
χ5622-222-222200-200-2000000−1−i3−1−i31+i3−1−i3−1−i31+i3−1−i3−1−i3−1−i3001+i3001+i3000000−1+i3−1+i31−i3−1+i3−1+i31−i3−1+i3−1+i3−1+i3001−i3001−i3000000
χ5722-2-12-2-1-1-1001−i3i31i3−i30000−1−i3−1−i31+i31+i32−1−i31+i31+i321+i321+i3200−1−i32−3+i323−i32−1−i323−i32−3+i320000−1+i3−1+i31−i31−i32−1+i31−i31−i321−i321−i3200−1+i323+i32−3−i32−1+i32−3−i323+i320000
χ5822-2-12-2-1-1-1001i3−i31−i3i30000−1−i3−1−i31+i31+i32−1−i31+i31+i321+i321+i3200−1−i323−i32−3+i32−1−i32−3+i323−i320000−1+i3−1+i31−i31−i32−1+i31−i31−i321−i321−i3200−1+i32−3−i323+i32−1+i323+i32−3−i320000
χ5922-2-1-22-1112-21-1-1-1110000−1−i3−1−i31+i31+i321+i3−1−i31+i32−1−i32−1−i32−1−i31+i3−1−i321+i321+i321+i32−1−i32−1−i320000−1+i3−1+i31−i31−i321−i3−1+i31−i32−1+i32−1+i32−1+i31−i3−1+i321−i321−i321−i32−1+i32−1+i320000
χ6022-2-1-22-111-22111-1-1-10000−1−i3−1−i31+i31+i321+i3−1−i31+i32−1−i32−1−i321+i3−1−i3−1−i32−1−i32−1−i321+i321+i321+i320000−1+i3−1+i31−i31−i321−i3−1+i31−i32−1+i32−1+i321−i3−1+i3−1+i32−1+i32−1+i321−i321−i321−i320000
χ614-40400-400000000000000−2−2i32+2i30−2−2i3002+2i300000000000000−2+2i32−2i30−2+2i3002−2i300000000000000
χ624-40-200223−23000000000000−2−2i32+2i301+i300−1−i34ζ7+2ζ11−4ζ7−2ζ11000000000000−2+2i32−2i301−i300−1+i3−2ζ7−4ζ112ζ7+4ζ11000000000000
χ634-40-2002−2323000000000000−2−2i32+2i301+i300−1−i3−4ζ7−2ζ114ζ7+2ζ11000000000000−2+2i32−2i301−i300−1+i32ζ7+4ζ11−2ζ7−4ζ11000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.