Finite Group Databasebeta

← Group #504136

Character table — Group #504136

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488881616161616161616161616161616161644444488881616161616161616224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ5111111111111111111111111-1-111-1-111111111111111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ6111111111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ7111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ8111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1
χ9111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-111-1-1-1-1-1-111111111-1-1-1-1-1-1-11
χ10111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111-1
χ11111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-111-1-11111-1-1-1-1-1-111-1-1-1-1111-1
χ12111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-11
χ13111111111-1-1-1-111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-1111111-1-1-1-111-1-1-1-111-1-11-1
χ14111111111-1-1-1-111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-11111-1-111-11
χ15111111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-111111-1-111-1-1-1-11111-1-1-1-1-1-11111-11
χ16111111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-1-1-11111111111-1-1-1-11-1
χ172222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-20000000000000000200002-2-2-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-20000000000000000-20000-2222200000000000000000000
χ19222222222-2-2-2-2222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000020000-2-2-22200000000000000000000
χ20222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000-20000222-2-200000000000000000000
χ2122222222-22222-2-2-20000000022-2-22200002222−2−2−2−22222−2−2−2−2-20000-2000022−2−222−2−2000000000000
χ2222222222-22222-2-2-20000000022-2-2220000−2−2−2−22222−2−2−2−22222-20000-20000−2−222−2−222000000000000
χ2322222222-22222-2-2-200000000-2-2-2-2-2-200002222−2−2−2−22222−2−2−2−22000020000−2−222−2−222000000000000
χ2422222222-22222-2-2-200000000-2-2-2-2-2-20000−2−2−2−22222−2−2−2−22222200002000022−2−222−2−2000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-200002222−2−2−2−2−2−2−2−22222-2000020000−2−22222−2−2000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-20000−2−2−2−222222222−2−2−2−2-200002000022−2−2−2−222000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-2222200002222−2−2−2−2−2−2−2−2222220000-2000022−2−2−2−222000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-222220000−2−2−2−222222222−2−2−2−220000-20000−2−22222−2−2000000000000
χ292222-2-2-2-2200002-2-22222-2-2-2-2000000000022-2-222-2-200000000022-2-200000000000002-20000000000
χ302222-2-2-2-2200002-2-22222-2-2-2-2000000000022-2-222-2-2000000000-2-2220000000000000-220000000000
χ312222-2-2-2-2200002-2-22222-2-2-2-20000000000-2-222-2-22200000000022-2-20000000000000-220000000000
χ322222-2-2-2-2200002-2-22222-2-2-2-20000000000-2-222-2-222000000000-2-22200000000000002-20000000000
χ3322-2-22-22-2022-2-20002−22−22−22−22-2002-222−2−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ50000002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ3422-2-22-22-2022-2-20002−22−22−22−22-2002-222−2−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ50000002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ3522-2-22-22-2022-2-20002−22−22−22−2-2200-2222−2−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000−22−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ3622-2-22-22-2022-2-20002−22−22−22−2-2200-2222−2−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000−22−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ3722-2-22-22-2022-2-2000−22−22−22−222-2002-2−2−222ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ3822-2-22-22-2022-2-2000−22−22−22−222-2002-2−2−222−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ3922-2-22-22-2022-2-2000−22−22−22−22-2200-22−2−222ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ70000002−22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ4022-2-22-22-2022-2-2000−22−22−22−22-2200-22−2−222−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ70000002−22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ4122-2-22-22-20-2-2220002−22−22−22−22-200-22−2−222ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ50000002−2−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4222-2-22-22-20-2-2220002−22−22−22−22-200-22−2−222−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ50000002−2−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4322-2-22-22-20-2-2220002−22−22−22−2-22002-2−2−222ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000−222−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4422-2-22-22-20-2-2220002−22−22−22−2-22002-2−2−222−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000−222−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4522-2-22-22-20-2-222000−22−22−22−222-200-2222−2−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000−222−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ4622-2-22-22-20-2-222000−22−22−22−222-200-2222−2−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000−222−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ4722-2-22-22-20-2-222000−22−22−22−22-22002-222−2−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ70000002−2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ4822-2-22-22-20-2-222000−22−22−22−22-22002-222−2−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ70000002−2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ492-2-2222-2-2-22i−2i2i−2i22-222-2-2-2-222002i−2i002i−2i2i−2i0000000000000000000000000000000000002-2002i−2i0000
χ502-2-2222-2-2-22i−2i2i−2i22-222-2-2-2-222002i−2i002i−2i2i−2i000000000000000000000000000000000000-2200−2i2i0000
χ512-2-2222-2-2-22i−2i2i−2i22-2-2-22222-2-2002i−2i00−2i2i−2i2i000000000000000002-22-2000000000000000002i−2i000000
χ522-2-2222-2-2-22i−2i2i−2i22-2-2-22222-2-2002i−2i00−2i2i−2i2i00000000000000000-22-2200000000000000000−2i2i000000
χ532-2-2222-2-2-2−2i2i−2i2i22-222-2-2-2-22200−2i2i00−2i2i−2i2i0000000000000000000000000000000000002-200−2i2i0000
χ542-2-2222-2-2-2−2i2i−2i2i22-222-2-2-2-22200−2i2i00−2i2i−2i2i000000000000000000000000000000000000-22002i−2i0000
χ552-2-2222-2-2-2−2i2i−2i2i22-2-2-22222-2-200−2i2i002i−2i2i−2i000000000000000002-22-200000000000000000−2i2i000000
χ562-2-2222-2-2-2−2i2i−2i2i22-2-2-22222-2-200−2i2i002i−2i2i−2i00000000000000000-22-22000000000000000002i−2i000000
χ572-2-22-2-222-200002-22-2-222-2-2220000000000000000002-22-22-22-202-2-220000000000000000000002-200
χ582-2-22-2-222-200002-22-2-222-2-2220000000000000000002-22-22-22-20-222-2000000000000000000000-2200
χ592-2-22-2-222-200002-22-2-222-2-222000000000000000000-22-22-22-2202-2-22000000000000000000000-2200
χ602-2-22-2-222-200002-22-2-222-2-222000000000000000000-22-22-22-220-222-20000000000000000000002-200
χ614444-4-4-4-4400004-4-4-4-4-4-4444400000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-40000-4440000000000000000002222−22−22−22−22222200000000000000000000000000000000000000
χ634444-4-4-4-4-40000-444000000000000000000−22−2222222222−22−2200000000000000000000000000000000000000
χ6444-4-4-44-440000000022−2222−22−2222−222200000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000000000
χ6544-4-4-44-440000000022−2222−22−2222−22220000000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000000000
χ6644-4-4-44-4400000000−2222−222222−2222−2200000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000000000
χ6744-4-4-44-4400000000−2222−222222−2222−220000000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000000000
χ684-44-44-4-4404i−4i−4i4i00022−22−2222−222222−220000002i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ694-44-44-4-4404i−4i−4i4i000−222222−2222−22−2222000000−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ704-44-44-4-440−4i4i4i−4i00022−22−2222−222222−22000000−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ714-44-44-4-440−4i4i4i−4i000−222222−2222−22−22220000002i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ724-44-4-444-40000000022−22−222222−22−22220000000000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7000000000000000000000000000000
χ734-44-4-444-40000000022−22−222222−22−2222000000000000000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ7000000000000000000000000000000
χ744-44-4-444-400000000−222222−22−222222−220000000000000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000000000
χ754-44-4-444-400000000−222222−22−222222−22000000000000000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000000000
χ764-4-4444-4-444i−4i4i−4i-4-440000000000−4i4i0000000000000000000000000000000000000000000000000000
χ774-4-4444-4-44−4i4i−4i4i-4-4400000000004i−4i0000000000000000000000000000000000000000000000000000
χ784-4-44-4-44440000-44-40000000000000000000000000022−2222−22−2222−2222000000000000000000000000000000
χ794-4-44-4-44440000-44-400000000000000000000000000−2222−222222−2222−22000000000000000000000000000000
χ804-4-44-4-444-400004-4444-4-444-4-400000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.