Finite Group Databasebeta

← Group #369489

Character table — Group #369489

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222444444444444444444444444888888888888888888888888888888888888161616161616
order12222222222244444444222244444444444488888888444444444444444444444444888888888888448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111
χ8111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111111111-1-1
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-11111-1-1111111-1-1-1-1
χ1711-11-1-11-111-1-111-1-1-1-11111-1-1ii−i−i11-1-1ii−i−iii−i−i11-1-1i−ii−iii−i−ii−i11-1-1i−iii−i−iii−i−ii−i11-1-11-111-1-11-1i−i1-1
χ1811-11-1-11-111-1-111-1-1-1-11111-1-1ii−i−i11-1-1ii−i−iii−i−i-1-111i−i−iiii−i−ii−i11-1-1−ii−i−iii−i−iiii−i11-1-1-11-1-111-11−ii-11
χ1911-11-1-11-111-1-111-1-1-1-11111-1-1ii−i−i11-1-1ii−i−i−i−iii11-1-1−iii−iii−i−i−ii-1-111i−iii−i−i−i−iii−ii-1-1111-111-1-1-11−ii-11
χ2011-11-1-11-111-1-111-1-1-1-11111-1-1ii−i−i11-1-1ii−i−i−i−iii-1-111−ii−iiii−i−i−ii-1-111−ii−i−iiiii−i−i−ii-1-111-11-1-1111-1i−i1-1
χ2111-11-1-11-111-1-111-1-1-1-11111-1-1−i−iii11-1-1−i−iiiii−i−i11-1-1i−i−ii−i−iiii−i-1-111−ii−i−iiiii−i−ii−i-1-1111-111-1-1-11i−i-11
χ2211-11-1-11-111-1-111-1-1-1-11111-1-1−i−iii11-1-1−i−iiiii−i−i-1-111i−ii−i−i−iiii−i-1-111i−iii−i−i−i−iiii−i-1-111-11-1-1111-1−ii1-1
χ2311-11-1-11-111-1-111-1-1-1-11111-1-1−i−iii11-1-1−i−iii−i−iii11-1-1−ii−ii−i−iii−ii11-1-1−ii−i−iii−i−iii−ii11-1-11-111-1-11-1−ii1-1
χ2411-11-1-11-111-1-111-1-1-1-11111-1-1−i−iii11-1-1−i−iii−i−iii-1-111−iii−i−i−iii−ii11-1-1i−iii−i−iii−i−i−ii11-1-1-11-1-111-11i−i-11
χ2511-11-1-11-111-1-111-1-1-1-111-1-111ii−i−i-1-111ii−i−iii−i−i11-1-1−iii−i−i−iii−ii-1-111i−i−i−iiiii−i−ii−i11-1-11-1-1-111-11−ii1-1
χ2611-11-1-11-111-1-111-1-1-1-111-1-111ii−i−i-1-111ii−i−iii−i−i-1-111−ii−ii−i−iii−ii-1-111−iiii−i−i−i−iiii−i11-1-1-1111-1-11-1i−i-11
χ2711-11-1-11-111-1-111-1-1-1-111-1-111ii−i−i-1-111ii−i−i−i−iii11-1-1i−ii−i−i−iiii−i11-1-1i−i−i−iii−i−iii−ii-1-1111-1-1-1111-1i−i-11
χ2811-11-1-11-111-1-111-1-1-1-111-1-111ii−i−i-1-111ii−i−i−i−iii-1-111i−i−ii−i−iiii−i11-1-1−iiii−i−iii−i−i−ii-1-111-1111-1-1-11−ii1-1
χ2911-11-1-11-111-1-111-1-1-1-111-1-111−i−iii-1-111−i−iiiii−i−i11-1-1−ii−iiii−i−i−ii11-1-1−iiii−i−iii−i−ii−i-1-1111-1-1-1111-1−ii-11
χ3011-11-1-11-111-1-111-1-1-1-111-1-111−i−iii-1-111−i−iiiii−i−i-1-111−iii−iii−i−i−ii11-1-1i−i−i−iii−i−iiii−i-1-111-1111-1-1-11i−i1-1
χ3111-11-1-11-111-1-111-1-1-1-111-1-111−i−iii-1-111−i−iii−i−iii11-1-1i−i−iiii−i−ii−i-1-111−iiii−i−i−i−iii−ii11-1-11-1-1-111-11i−i1-1
χ3211-11-1-11-111-1-111-1-1-1-111-1-111−i−iii-1-111−i−iii−i−iii-1-111i−ii−iii−i−ii−i-1-111i−i−i−iiiii−i−i−ii11-1-1-1111-1-11-1−ii-11
χ3322222222-2-2-2-22-22-22-22-2000022220000-2-2-2-20000222200220000000000-2-200000000000000-2-20000000000
χ3422222222-2-2-2-22-22-22-22-2000022220000-2-2-2-20000-2-2-2-200-2-200000000002200000000000000220000000000
χ3522222222-2-2-2-22-22-22-22-20000-2-2-2-2000022220000222200-2-200000000002200000000000000-2-20000000000
χ3622222222-2-2-2-22-22-22-22-20000-2-2-2-2000022220000-2-2-2-200220000000000-2-200000000000000220000000000
χ3722222222-2-2-2-2-22-22-22-2222220000-2-2-2-200002222000022000000-2-200000000000000-2-20000000000000000
χ3822222222-2-2-2-2-22-22-22-2222220000-2-2-2-20000-2-2-2-20000-2-20000002200000000000000220000000000000000
χ3922222222-2-2-2-2-22-22-22-22-2-2-2-200002222000022220000-2-20000002200000000000000-2-20000000000000000
χ4022222222-2-2-2-2-22-22-22-22-2-2-2-2000022220000-2-2-2-2000022000000-2-200000000000000220000000000000000
χ4122-22-2-22-2-2-2222-2-22-222-200002i2i−2i−2i0000−2i−2i2i2i000022-2-2002i−2i0000000000−2i2i00000000000000-220000000000
χ4222-22-2-22-2-2-2222-2-22-222-200002i2i−2i−2i0000−2i−2i2i2i0000-2-22200−2i2i00000000002i−2i000000000000002-20000000000
χ4322-22-2-22-2-2-2222-2-22-222-20000−2i−2i2i2i00002i2i−2i−2i000022-2-200−2i2i00000000002i−2i00000000000000-220000000000
χ4422-22-2-22-2-2-2222-2-22-222-20000−2i−2i2i2i00002i2i−2i−2i0000-2-222002i−2i0000000000−2i2i000000000000002-20000000000
χ4522-22-2-22-2-2-222-222-22-2-2222-2-20000-2-22200002i2i−2i−2i00002i−2i000000−2i2i00000000000000−2i2i0000000000000000
χ4622-22-2-22-2-2-222-222-22-2-2222-2-20000-2-2220000−2i−2i2i2i0000−2i2i0000002i−2i000000000000002i−2i0000000000000000
χ4722-22-2-22-2-2-222-222-22-2-22-2-222000022-2-200002i2i−2i−2i0000−2i2i0000002i−2i00000000000000−2i2i0000000000000000
χ4822-22-2-22-2-2-222-222-22-2-22-2-222000022-2-20000−2i−2i2i2i00002i−2i000000−2i2i000000000000002i−2i0000000000000000
χ492-222-22-2-22-22-22222-2-2-2-22-22-22-22-22-22-22-22-20000000000002-22-20000000000000000000000000000000000
χ502-222-22-2-22-22-22222-2-2-2-22-22-2-22-222-22-2-22-22000000000000-22-220000000000000000000000000000000000
χ512-222-22-2-22-22-22222-2-2-2-2-22-222-22-2-22-222-22-2000000000000-22-220000000000000000000000000000000000
χ522-222-22-2-22-22-22222-2-2-2-2-22-22-22-22-22-22-22-220000000000002-22-20000000000000000000000000000000000
χ532-222-22-2-2-22-222-22-2-22-2200002-22-20000-22-220000000000000000000000002i−2i2i−2i0000000000002i−2i2i−2i000000
χ542-222-22-2-2-22-222-22-2-22-2200002-22-20000-22-22000000000000000000000000−2i2i−2i2i000000000000−2i2i−2i2i000000
χ552-222-22-2-2-22-222-22-2-22-220000-22-2200002-22-20000000000000000000000002i−2i2i−2i000000000000−2i2i−2i2i000000
χ562-222-22-2-2-22-222-22-2-22-220000-22-2200002-22-2000000000000000000000000−2i2i−2i2i0000000000002i−2i2i−2i000000
χ572-222-22-2-2-22-22-22-222-22-22-22-20000-22-2200000000000000000000002i−2i2i−2i0000000000002i−2i2i−2i000000000000
χ582-222-22-2-2-22-22-22-222-22-22-22-20000-22-220000000000000000000000−2i2i−2i2i000000000000−2i2i−2i2i000000000000
χ592-222-22-2-2-22-22-22-222-22-2-22-2200002-22-200000000000000000000002i−2i2i−2i000000000000−2i2i−2i2i000000000000
χ602-222-22-2-2-22-22-22-222-22-2-22-2200002-22-20000000000000000000000−2i2i−2i2i0000000000002i−2i2i−2i000000000000
χ612-2-222-2-222-2-2222-2-222-2-22-2-222i−2i−2i2i2-2-222i−2i−2i2i0000000000002i−2i−2i2i0000000000000000000000000000000000
χ622-2-222-2-222-2-2222-2-222-2-22-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000000000−2i2i2i−2i0000000000000000000000000000000000
χ632-2-222-2-222-2-2222-2-222-2-2-222-22i−2i−2i2i-222-22i−2i−2i2i000000000000−2i2i2i−2i0000000000000000000000000000000000
χ642-2-222-2-222-2-2222-2-222-2-2-222-2−2i2i2i−2i-222-2−2i2i2i−2i0000000000002i−2i−2i2i0000000000000000000000000000000000
χ652-2-222-2-22-222-22-2-222-2-2200002i−2i−2i2i0000−2i2i2i−2i0000000000000000000000002-2-22000000000000−2i2i2i−2i000000
χ662-2-222-2-22-222-22-2-222-2-2200002i−2i−2i2i0000−2i2i2i−2i000000000000000000000000-222-20000000000002i−2i−2i2i000000
χ672-2-222-2-22-222-22-2-222-2-220000−2i2i2i−2i00002i−2i−2i2i0000000000000000000000002-2-220000000000002i−2i−2i2i000000
χ682-2-222-2-22-222-22-2-222-2-220000−2i2i2i−2i00002i−2i−2i2i000000000000000000000000-222-2000000000000−2i2i2i−2i000000
χ692-2-222-2-22-222-2-222-2-222-22-2-220000-222-200000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i000000000000
χ702-2-222-2-22-222-2-222-2-222-22-2-220000-222-20000000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i000000000000
χ712-2-222-2-22-222-2-222-2-222-2-222-200002-2-2200000000000000000000002i−2i−2i2i000000000000−2i2i2i−2i000000000000
χ722-2-222-2-22-222-2-222-2-222-2-222-200002-2-220000000000000000000000−2i2i2i−2i0000000000002i−2i−2i2i000000000000
χ73444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000000000
χ74444-44-4-4-4000000000000000000000000000022−2222−2222−2222−22000000000000000000002-22-2000000000000000000
χ75444-44-4-4-4000000000000000000000000000022−2222−22−2222−222200000000000000000000-22-22000000000000000000
χ76444-44-4-4-40000000000000000000000000000−2222−222222−2222−2200000000000000000000-22-22000000000000000000
χ77444-44-4-4-40000000000000000000000000000−2222−2222−2222−2222000000000000000000002-22-2000000000000000000
χ7844-44-4-44-444-4-4-4-44444-4-4000000000000000000000000000000000000000000000000000000000000000000
χ7944-4-4-44-4400000000000000000000000000002i2−2i2−2i22i222−22−2222000000000000000000002i−2i−2i2i000000000000000000
χ8044-4-4-44-4400000000000000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000−2i2i2i−2i000000000000000000
χ8144-4-4-44-440000000000000000000000000000−2i22i22i2−2i222−22−222200000000000000000000−2i2i2i−2i000000000000000000
χ8244-4-4-44-440000000000000000000000000000−2i22i22i2−2i2−222222−22000000000000000000002i−2i−2i2i000000000000000000
χ834-444-44-4-44-44-4-4-4-4-44444000000000000000000000000000000000000000000000000000000000000000000
χ844-4-444-4-444-4-44-4-444-4-444000000000000000000000000000000000000000000000000000000000000000000
χ858-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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