Finite Group Databasebeta

← Group #481483

Character table — Group #481483

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222222222222244444444444444448888888888888888888888888888888888888888161616161616
order12222222222222444422444444444444444444444488888888888888888888888888888888244444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ311111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i111-1-1-1
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii111-1-1-1
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1111
χ9111111111-1-1-1-11-1-1-1-1111111-1-111-1-1-1-1-1-1-111-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-111-1
χ10111111111-1-1-1-11-1-1-1-1111111-1-111-1-1-1-1-1-1-111-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-111-1
χ11111111111-1-1-1-11-1-1-1-1111111-1-111-1-1-1-1-1-1-111-1-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-11-1-11
χ12111111111-1-1-1-11-1-1-1-1111111-1-111-1-1-1-1-1-1-111-1-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-11-1-11
χ13111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-111-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-1-11
χ14111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-111-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1-11
χ15111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1111-1
χ16111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-111-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1111-1
χ1711111-1-1-1-111111-1-1-1-11111-1-111-1-111-1-1-1-1-11-1111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i-1-111-11
χ1811111-1-1-1-111111-1-1-1-11111-1-111-1-111-1-1-1-1-11-1111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii-1-111-11
χ1911111-1-1-1-111111-1-1-1-11111-1-111-1-111-1-1-1-1-11-11-1-111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii11-1-11-1
χ2011111-1-1-1-111111-1-1-1-11111-1-111-1-111-1-1-1-1-11-11-1-111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i11-1-11-1
χ2111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-11111-11-11111111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-111-1-11-11-1
χ2211111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-11111-11-111111-1-111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-11-11-1
χ2311111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-11111-11-11-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-11111-1-111-1-111-11-11
χ2411111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-11111-11-11-1-1-1-1-1-111-1-11111-1-111-1-111-1-111-1-1-1-111-1-11111-11-11
χ2511111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-11-1-1
χ2611111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-11-1-1
χ2711111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-111-111
χ2811111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-111-111
χ2911111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-111-1-111-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-1-111
χ3011111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-111-1-111-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-1-111
χ3111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-1111-1-1
χ3211111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-1111-1-1
χ3322222222222222222222-2-2-2-2-2-222222-2-22-2-2-2-2000000000000000000000000000000000000000000
χ34222222222222222222-2-2222222-2-2-2-2-222-2-2-2-2-2000000000000000000000000000000000000000000
χ35222222222-2-2-2-22-2-2-2-222-2-2-2-22222-2-2-222-22-2-22000000000000000000000000000000000000000000
χ36222222222-2-2-2-22-2-2-2-2-2-22222-2-2-2-2222-2-222-2-22000000000000000000000000000000000000000000
χ3722222-2-2-2-222222-2-2-2-222-2-222-2-2-2-222-222-22-22-2000000000000000000000000000000000000000000
χ3822222-2-2-2-222222-2-2-2-2-2-222-2-22222-2-22-2-222-22-2000000000000000000000000000000000000000000
χ3922222-2-2-2-2-2-2-2-22222222-2-22222-2-2-2-22-2-22-2-222000000000000000000000000000000000000000000
χ4022222-2-2-2-2-2-2-2-222222-2-222-2-2-2-22222-222-2-2-222000000000000000000000000000000000000000000
χ412-2-22222-2-222-2-2-222-2-2002i−2i2i−2i2i−2i000002i−2i00000000000000000000000001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i000000
χ422-2-22222-2-222-2-2-222-2-2002i−2i2i−2i2i−2i000002i−2i0000000000000000000000000−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i000000
χ432-2-22222-2-222-2-2-222-2-200−2i2i−2i2i−2i2i00000−2i2i00000000000000000000000001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i000000
χ442-2-22222-2-222-2-2-222-2-200−2i2i−2i2i−2i2i00000−2i2i0000000000000000000000000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i000000
χ452-2-22222-2-2-2-222-2-2-222002i−2i2i−2i−2i2i00000−2i2i00000000000000000000000001−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i000000
χ462-2-22222-2-2-2-222-2-2-222002i−2i2i−2i−2i2i00000−2i2i0000000000000000000000000−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i000000
χ472-2-22222-2-2-2-222-2-2-22200−2i2i−2i2i2i−2i000002i−2i00000000000000000000000001+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i000000
χ482-2-22222-2-2-2-222-2-2-22200−2i2i−2i2i2i−2i000002i−2i0000000000000000000000000−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i000000
χ492-2-222-2-22222-2-2-2-2-222002i−2i−2i2i2i−2i00000−2i2i00000000000000000000000001−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i000000
χ502-2-222-2-22222-2-2-2-2-222002i−2i−2i2i2i−2i00000−2i2i0000000000000000000000000−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i000000
χ512-2-222-2-22222-2-2-2-2-22200−2i2i2i−2i−2i2i000002i−2i00000000000000000000000001+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i000000
χ522-2-222-2-22222-2-2-2-2-22200−2i2i2i−2i−2i2i000002i−2i0000000000000000000000000−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i000000
χ532-2-222-2-222-2-222-222-2-2002i−2i−2i2i−2i2i000002i−2i00000000000000000000000001+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i000000
χ542-2-222-2-222-2-222-222-2-2002i−2i−2i2i−2i2i000002i−2i0000000000000000000000000−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i000000
χ552-2-222-2-222-2-222-222-2-200−2i2i2i−2i2i−2i00000−2i2i00000000000000000000000001−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i000000
χ562-2-222-2-222-2-222-222-2-200−2i2i2i−2i2i−2i00000−2i2i0000000000000000000000000−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i000000
χ572-2-22-22-22-22-22-222-22-22-20000002-22-2200-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000000000
χ582-2-22-22-22-22-22-222-22-22-20000002-22-2200-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000000000
χ592-2-22-22-22-22-22-222-22-2-22000000-22-22-2002000000002−22−22−22−2−22−22−22−220000000000000000000000
χ602-2-22-22-22-22-22-222-22-2-22000000-22-22-200200000000−22−22−22−222−22−22−22−20000000000000000000000
χ612-2-22-22-22-2-22-222-22-222-20000002-2-22-2002000000002−22−2−22−222−22−2−22−220000000000000000000000
χ622-2-22-22-22-2-22-222-22-222-20000002-2-22-200200000000−22−222−22−2−22−222−22−20000000000000000000000
χ632-2-22-22-22-2-22-222-22-22-22000000-222-2200-200000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000000000
χ642-2-22-22-22-2-22-222-22-22-22000000-222-2200-200000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000000000
χ652-2-22-2-22-222-22-22-22-222-2000000-222-2-2002000000002−2−222−2−222−2−222−2−220000000000000000000000
χ662-2-22-2-22-222-22-22-22-222-2000000-222-2-200200000000−222−2−222−2−222−2−222−20000000000000000000000
χ672-2-22-2-22-222-22-22-22-22-220000002-2-22200-200000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000000000
χ682-2-22-2-22-222-22-22-22-22-220000002-2-22200-200000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000000000
χ692-2-22-2-22-22-22-2222-22-22-2000000-22-22200-200000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000000000
χ702-2-22-2-22-22-22-2222-22-22-2000000-22-22200-200000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000000000
χ712-2-22-2-22-22-22-2222-22-2-220000002-22-2-2002000000002−2−22−222−2−222−22−2−220000000000000000000000
χ722-2-22-2-22-22-22-2222-22-2-220000002-22-2-200200000000−222−22−2−222−2−22−222−20000000000000000000000
χ734444-44-4-444-4-44-44-4-4400000000000000000000000000000000000000000000000000000000000000
χ744444-44-4-44-444-4-4-444-400000000000000000000000000000000000000000000000000000000000000
χ754444-4-444-44-4-44-4-444-400000000000000000000000000000000000000000000000000000000000000
χ764444-4-444-4-444-4-44-4-4400000000000000000000000000000000000000000000000000000000000000
χ7788-8-80000000000000000000000000000000000004-400000000000000000000000000000000000000
χ7888-8-8000000000000000000000000000000000000-4400000000000000000000000000000000000000
χ798-88-800000000000000000000000000000000004i−4i0000000000000000000000000000000000000000
χ808-88-80000000000000000000000000000000000−4i4i0000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).