Finite Group Databasebeta

← Group #227274

Character table — Group #227274

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888822224444448888888888888888888844444444444488888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-11-1-1-1-1111111111111111111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-11111-1-1-1-111-1-111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1111111-1-111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-11111-1-1-1-111
χ171-1-11-11-1111-1-111-1-1iiii−i−i−i−i11-1-1-1ii−i−i1ii−i−iii−i−iii−i−i1111-1-1-1-1i−ii−i1-1i−i1-11-111-1-1ii−i−ii−i1-1i−i1-11-1i−i
χ181-1-11-11-1111-1-111-1-1iiii−i−i−i−i11-1-1-1ii−i−i1ii−i−iii−i−iii−i−i1111-1-1-1-1i−i−ii-11−ii1-1-1111-1-1ii−i−i−ii-11−ii-11-11−ii
χ191-1-11-11-1111-1-111-1-1iiii−i−i−i−i11-1-1-1−i−iii1ii−i−i−i−iii−i−iii-1-1-1-11111−iii−i1-1i−i1-11-1-1-111ii−i−i−ii-11i−i1-1-11−ii
χ201-1-11-11-1111-1-111-1-1iiii−i−i−i−i11-1-1-1−i−iii1ii−i−i−i−iii−i−iii-1-1-1-11111−ii−ii-11−ii1-1-11-1-111ii−i−ii−i1-1−ii-111-1i−i
χ211-1-11-11-1111-1-111-1-1iiii−i−i−i−i-1-111-1ii−i−i1ii−i−i−i−iii−i−iii-1-1-1-11111i−ii−i1-1i−i-111-111-1-1−i−iiii−i1-1−ii-11-11−ii
χ221-1-11-11-1111-1-111-1-1iiii−i−i−i−i-1-111-1ii−i−i1ii−i−i−i−iii−i−iii-1-1-1-11111i−i−ii-11−ii-11-1111-1-1−i−iii−ii-11i−i1-11-1i−i
χ231-1-11-11-1111-1-111-1-1iiii−i−i−i−i-1-111-1−i−iii1ii−i−iii−i−iii−i−i1111-1-1-1-1−iii−i1-1i−i-111-1-1-111−i−iii−ii-11−ii-111-1i−i
χ241-1-11-11-1111-1-111-1-1iiii−i−i−i−i-1-111-1−i−iii1ii−i−iii−i−iii−i−i1111-1-1-1-1−ii−ii-11−ii-11-11-1-111−i−iiii−i1-1i−i1-1-11−ii
χ251-1-11-11-1111-1-111-1-1−i−i−i−iiiii11-1-1-1ii−i−i1−i−iiiii−i−iii−i−i-1-1-1-11111i−ii−i-11i−i1-1-11-1-111−i−iii−ii1-1i−i-111-1−ii
χ261-1-11-11-1111-1-111-1-1−i−i−i−iiiii11-1-1-1ii−i−i1−i−iiiii−i−iii−i−i-1-1-1-11111i−i−ii1-1−ii1-11-1-1-111−i−iiii−i-11−ii1-1-11i−i
χ271-1-11-11-1111-1-111-1-1−i−i−i−iiiii11-1-1-1−i−iii1−i−iii−i−iii−i−iii1111-1-1-1-1−iii−i-11i−i1-1-1111-1-1−i−iiii−i-11i−i-11-11i−i
χ281-1-11-11-1111-1-111-1-1−i−i−i−iiiii11-1-1-1−i−iii1−i−iii−i−iii−i−iii1111-1-1-1-1−ii−ii1-1−ii1-11-111-1-1−i−iii−ii1-1−ii1-11-1−ii
χ291-1-11-11-1111-1-111-1-1−i−i−i−iiiii-1-111-1ii−i−i1−i−iii−i−iii−i−iii1111-1-1-1-1i−ii−i-11i−i-11-11-1-111ii−i−i−ii1-1−ii1-1-11i−i
χ301-1-11-11-1111-1-111-1-1−i−i−i−iiiii-1-111-1ii−i−i1−i−iii−i−iii−i−iii1111-1-1-1-1i−i−ii1-1−ii-111-1-1-111ii−i−ii−i-11i−i-111-1−ii
χ311-1-11-11-1111-1-111-1-1−i−i−i−iiiii-1-111-1−i−iii1−i−iiiii−i−iii−i−i-1-1-1-11111−iii−i-11i−i-11-1111-1-1ii−i−ii−i-11−ii1-11-1−ii
χ321-1-11-11-1111-1-111-1-1−i−i−i−iiiii-1-111-1−i−iii1−i−iiiii−i−iii−i−i-1-1-1-11111−ii−ii1-1−ii-111-111-1-1ii−i−i−ii1-1i−i-11-11i−i
χ33222222222-22-22-22-2000000002222-22222-200002222-2-2-2-200000000-2-2000000-2-20000000000000000000000
χ34222222222-22-22-22-2000000002222-2-2-2-2-2-20000-2-2-2-222220000000022000000-2-20000000000000000000000
χ35222222222-22-22-22-200000000-2-2-2-2-22222-20000-2-2-2-2222200000000-2-2000000220000000000000000000000
χ36222222222-22-22-22-200000000-2-2-2-2-2-2-2-2-2-200002222-2-2-2-20000000022000000220000000000000000000000
χ3722222222-22-22-22-22222222220000-20000-2-2-2-2-20000000000000000002222-2-200-2-200000000000000000000
χ3822222222-22-22-22-22222222220000-20000-2-2-2-2-2000000000000000000-2-2-2-222002200000000000000000000
χ3922222222-22-22-22-22-2-2-2-2-2-2-2-20000-20000-2222200000000000000000022-2-2-2-2002200000000000000000000
χ4022222222-22-22-22-22-2-2-2-2-2-2-2-20000-20000-22222000000000000000000-2-2222200-2-200000000000000000000
χ4122-2-222-2-2-20-20202022−2−222−2−22-22-202i−2i2i−2i02−22−22i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i22−22−2000000000000
χ4222-2-222-2-2-20-20202022−2−222−2−22-22-20−2i2i−2i2i02−22−2−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i22−22−2000000000000
χ4322-2-222-2-2-20-20202022−2−222−2−2-22-2202i−2i2i−2i02−22−2−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2−22−22000000000000
χ4422-2-222-2-2-20-20202022−2−222−2−2-22-220−2i2i−2i2i02−22−22i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2−22−22000000000000
χ4522-2-222-2-2-20-202020−2−222−2−2222-22-202i−2i2i−2i0−22−222i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2−22−22000000000000
χ4622-2-222-2-2-20-202020−2−222−2−2222-22-20−2i2i−2i2i0−22−22−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2−22−22000000000000
χ4722-2-222-2-2-20-202020−2−222−2−222-22-2202i−2i2i−2i0−22−22−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i22−22−2000000000000
χ4822-2-222-2-2-20-202020−2−222−2−222-22-220−2i2i−2i2i0−22−222i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i22−22−2000000000000
χ492-22-2-222-2-202020-20i2i2−i2−i2−i2−i2i2i22-2-2202-2-220i2−i2−i2i22-2-220000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ502-22-2-222-2-202020-20i2i2−i2−i2−i2−i2i2i22-2-220-222-20i2−i2−i2i2-222-20000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ512-22-2-222-2-202020-20i2i2−i2−i2−i2−i2i2i2-222-202-2-220i2−i2−i2i2-222-20000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ522-22-2-222-2-202020-20i2i2−i2−i2−i2−i2i2i2-222-20-222-20i2−i2−i2i22-2-220000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ532-22-2-222-2-202020-20−i2−i2i2i2i2i2−i2−i22-2-2202-2-220−i2i2i2−i22-2-220000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ542-22-2-222-2-202020-20−i2−i2i2i2i2i2−i2−i22-2-220-222-20−i2i2i2−i2-222-20000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ552-22-2-222-2-202020-20−i2−i2i2i2i2i2−i2−i2-222-202-2-220−i2i2i2−i2-222-20000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ562-22-2-222-2-202020-20−i2−i2i2i2i2i2−i2−i2-222-20-222-20−i2i2i2−i22-2-220000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ572-2-22-22-222-2-222-2-220000000022-2-222i2i−2i−2i-200002i2i−2i−2i−2i−2i2i2i00000000−2i2i000000-220000000000000000000000
χ582-2-22-22-222-2-222-2-220000000022-2-22−2i−2i2i2i-20000−2i−2i2i2i2i2i−2i−2i000000002i−2i000000-220000000000000000000000
χ592-2-22-22-222-2-222-2-2200000000-2-22222i2i−2i−2i-20000−2i−2i2i2i2i2i−2i−2i00000000−2i2i0000002-20000000000000000000000
χ602-2-22-22-222-2-222-2-2200000000-2-2222−2i−2i2i2i-200002i2i−2i−2i−2i−2i2i2i000000002i−2i0000002-20000000000000000000000
χ612-2-22-22-22-222-2-222-22i2i2i2i−2i−2i−2i−2i000020000-2−2i−2i2i2i0000000000000000002i−2i2-2−2i2i00-2200000000000000000000
χ622-2-22-22-22-222-2-222-22i2i2i2i−2i−2i−2i−2i000020000-2−2i−2i2i2i000000000000000000−2i2i-222i−2i002-200000000000000000000
χ632-2-22-22-22-222-2-222-2−2i−2i−2i−2i2i2i2i2i000020000-22i2i−2i−2i0000000000000000002i−2i-22−2i2i002-200000000000000000000
χ642-2-22-22-22-222-2-222-2−2i−2i−2i−2i2i2i2i2i000020000-22i2i−2i−2i000000000000000000−2i2i2-22i−2i00-2200000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000000000004000040000000000000000000000000000000000000000000000000000
χ664444-4-4-4-40000000022−2222−2222−2222−2200000000000000000022−2222−222-22-22-22-200000000000000000000000000000000
χ674444-4-4-4-40000000022−2222−2222−2222−22000000000000000000−2222−2222-22-22-22-2200000000000000000000000000000000
χ684444-4-4-4-400000000−2222−2222−2222−222200000000000000000022−2222−22-22-22-22-2200000000000000000000000000000000
χ694444-4-4-4-400000000−2222−2222−2222−2222000000000000000000−2222−22222-22-22-22-200000000000000000000000000000000
χ7044-4-444-4-44040-40-402222−22−222222−22−220000000000−2222−2222000000000000000000000000000000000000000000000000
χ7144-4-444-4-44040-40-40−22−222222−22−222222000000000022−2222−22000000000000000000000000000000000000000000000000
χ7244-4-4-4-44404040-40-40000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ7344-4-4-4-44404040-40-4000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ7444-4-4-4-4440-40-404044-4-444-4-4400000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-4-4440-40-40404-444-4-444-400000000000000000000000000000000000000000000000000000000000000
χ764-44-44-4-44040-40-4040000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000
χ774-44-44-4-44040-40-404000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000
χ784-44-44-4-440-404040-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ794-44-44-4-440-404040-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ804-44-4-444-440-40-40402i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ814-44-4-444-440-40-4040−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ824-4-444-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000002i2−2i2−2i22i22-22-2-22-2200000000000000000000000000000000
χ834-4-444-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000−2i22i22i2−2i2-22-222-22-200000000000000000000000000000000
χ844-4-444-44-400000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000002i2−2i2−2i22i2-22-222-22-200000000000000000000000000000000
χ854-4-444-44-400000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000−2i22i22i2−2i22-22-2-22-2200000000000000000000000000000000
χ864-4-44-44-44-4-444-4-444000000000000-4000040000000000000000000000000000000000000000000000000000

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