Finite Group Databasebeta

← Group #229417

Character table — Group #229417

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888844444444448888888888888888888844444444444488888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111
χ7111111111111111111111111-1-1-1-11-1-1-1-1111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ91111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111111-1-111-1-1-1-111
χ1711-1-1-1-111-11-1-1-11111111-1-1-1-1ii−i−i111-1-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−ii−ii−ii−ii−ii−i1-1ii−i−i11-1-1i−ii−i1-11-11-11-1
χ1811-1-1-1-111-11-1-1-11111111-1-1-1-1ii−i−i111-1-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−ii−i−ii−ii−ii−ii1-1ii−i−i11-1-1−ii−ii-11-11-11-11
χ1911-1-1-1-111-11-1-1-11111111-1-1-1-1ii−i−i1-1-111-1−i−i−i−iiiii11-1-1−i−i−i−iiiiii−ii−ii−ii−ii−i-11ii−i−i-1-111−ii−ii1-11-1-11-11
χ2011-1-1-1-111-11-1-1-11111111-1-1-1-1ii−i−i1-1-111-1−i−i−i−iiiii11-1-1−i−i−i−iiiiii−i−ii−ii−ii−ii-11ii−i−i-1-111i−ii−i-11-111-11-1
χ2111-1-1-1-111-11-1-1-11111111-1-1-1-1−i−iii111-1-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii−iii−ii−ii−ii−i1-1−i−iii11-1-1i−ii−i-11-11-11-11
χ2211-1-1-1-111-11-1-1-11111111-1-1-1-1−i−iii111-1-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii−ii−ii−ii−ii−ii1-1−i−iii11-1-1−ii−ii1-11-11-11-1
χ2311-1-1-1-111-11-1-1-11111111-1-1-1-1−i−iii1-1-111-1iiii−i−i−i−i11-1-1iiii−i−i−i−i−iii−ii−ii−ii−i-11−i−iii-1-111−ii−ii-11-111-11-1
χ2411-1-1-1-111-11-1-1-11111111-1-1-1-1−i−iii1-1-111-1iiii−i−i−i−i11-1-1iiii−i−i−i−i−ii−ii−ii−ii−ii-11−i−iii-1-111i−ii−i1-11-1-11-11
χ2511-1-1-1-111-11-1-1-1111-1-1-1-11111ii−i−i111-1-1-1iiii−i−i−i−i-1-111−i−i−i−iiiiii−ii−i−iii−i−ii1-1−i−iii-1-111i−i−ii1-1-111-1-11
χ2611-1-1-1-111-11-1-1-1111-1-1-1-11111ii−i−i111-1-1-1iiii−i−i−i−i-1-111−i−i−i−iiiiii−i−iii−i−iii−i1-1−i−iii-1-111−iii−i-111-1-111-1
χ2711-1-1-1-111-11-1-1-1111-1-1-1-11111ii−i−i1-1-111-1−i−i−i−iiiii-1-111iiii−i−i−i−ii−ii−i−iii−i−ii-11−i−iii11-1-1−iii−i1-1-11-111-1
χ2811-1-1-1-111-11-1-1-1111-1-1-1-11111ii−i−i1-1-111-1−i−i−i−iiiii-1-111iiii−i−i−i−ii−i−iii−i−iii−i-11−i−iii11-1-1i−i−ii-111-11-1-11
χ2911-1-1-1-111-11-1-1-1111-1-1-1-11111−i−iii111-1-1-1−i−i−i−iiiii-1-111iiii−i−i−i−i−iii−i−iii−i−ii1-1ii−i−i-1-111i−i−ii-111-1-111-1
χ3011-1-1-1-111-11-1-1-1111-1-1-1-11111−i−iii111-1-1-1−i−i−i−iiiii-1-111iiii−i−i−i−i−ii−iii−i−iii−i1-1ii−i−i-1-111−iii−i1-1-111-1-11
χ3111-1-1-1-111-11-1-1-1111-1-1-1-11111−i−iii1-1-111-1iiii−i−i−i−i-1-111−i−i−i−iiiii−iii−i−iii−i−ii-11ii−i−i11-1-1−iii−i-111-11-1-11
χ3211-1-1-1-111-11-1-1-1111-1-1-1-11111−i−iii1-1-111-1iiii−i−i−i−i-1-111−i−i−i−iiiii−ii−iii−i−iii−i-11ii−i−i11-1-1i−i−ii1-1-11-111-1
χ332222222222-2-22-2-22222222220000-20000-200000000-2-2-2-200000000002222-2-2-2-20000000000000000000000
χ342222222222-2-22-2-22222222220000-20000-200000000-2-2-2-20000000000-2-2-2-222220000000000000000000000
χ352222222222-2-22-2-22-2-2-2-2-2-2-2-20000-20000-2000000002222000000000022-2-2-2-2220000000000000000000000
χ362222222222-2-22-2-22-2-2-2-2-2-2-2-20000-20000-20000000022220000000000-2-22222-2-20000000000000000000000
χ3722222222-2-222-222-2000000002222-22222-222-2-222-2-2000000000000-2-200000000-2-200000000000000000000
χ3822222222-2-222-222-2000000002222-2-2-2-2-2-2-2-222-2-222000000000000-2-2000000002200000000000000000000
χ3922222222-2-222-222-200000000-2-2-2-2-22222-2-2-222-2-2220000000000002200000000-2-200000000000000000000
χ4022222222-2-222-222-200000000-2-2-2-2-2-2-2-2-2-222-2-222-2-200000000000022000000002200000000000000000000
χ4122-2-2-2-2222-2-2-2222-2000000002i2i−2i−2i-222-2-222i2i−2i−2i−2i−2i2i2i000000000000−2i2i00000000-2200000000000000000000
χ4222-2-2-2-2222-2-2-2222-2000000002i2i−2i−2i-2-2-2222−2i−2i2i2i2i2i−2i−2i000000000000−2i2i000000002-200000000000000000000
χ4322-2-2-2-2222-2-2-2222-200000000−2i−2i2i2i-222-2-22−2i−2i2i2i2i2i−2i−2i0000000000002i−2i00000000-2200000000000000000000
χ4422-2-2-2-2222-2-2-2222-200000000−2i−2i2i2i-2-2-22222i2i−2i−2i−2i−2i2i2i0000000000002i−2i000000002-200000000000000000000
χ4522-2-2-2-222-2222-2-2-222222-2-2-2-20000-20000200000000-2-22200000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ4622-2-2-2-222-2222-2-2-222222-2-2-2-20000-20000200000000-2-2220000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ4722-2-2-2-222-2222-2-2-22-2-2-2-222220000-2000020000000022-2-200000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ4822-2-2-2-222-2222-2-2-22-2-2-2-222220000-2000020000000022-2-20000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ492-22-22-22-2002-202-20i2i2−i2−i2i2i2−i2−i22-22-202i−2i2i−2i02i−2i002i−2i00i2−i2i2−i222−2−222−2−2000000000000i2−i2i2−i22−22−2000000000000
χ502-22-22-22-2002-202-20i2i2−i2−i2i2i2−i2−i22-22-20−2i2i−2i2i0−2i2i00−2i2i00i2−i2i2−i2−2−222−2−222000000000000i2−i2i2−i2−22−22000000000000
χ512-22-22-22-2002-202-20i2i2−i2−i2i2i2−i2−i2-22-2202i−2i2i−2i0−2i2i00−2i2i00i2−i2i2−i2−2−222−2−222000000000000−i2i2−i2i22−22−2000000000000
χ522-22-22-22-2002-202-20i2i2−i2−i2i2i2−i2−i2-22-220−2i2i−2i2i02i−2i002i−2i00i2−i2i2−i222−2−222−2−2000000000000−i2i2−i2i2−22−22000000000000
χ532-22-22-22-2002-202-20−i2−i2i2i2−i2−i2i2i22-22-202i−2i2i−2i02i−2i002i−2i00−i2i2−i2i2−2−222−2−222000000000000−i2i2−i2i2−22−22000000000000
χ542-22-22-22-2002-202-20−i2−i2i2i2−i2−i2i2i22-22-20−2i2i−2i2i0−2i2i00−2i2i00−i2i2−i2i222−2−222−2−2000000000000−i2i2−i2i22−22−2000000000000
χ552-22-22-22-2002-202-20−i2−i2i2i2−i2−i2i2i2-22-2202i−2i2i−2i0−2i2i00−2i2i00−i2i2−i2i222−2−222−2−2000000000000i2−i2i2−i2−22−22000000000000
χ562-22-22-22-2002-202-20−i2−i2i2i2−i2−i2i2i2-22-220−2i2i−2i2i02i−2i002i−2i00−i2i2−i2i2−2−222−2−222000000000000i2−i2i2−i22−22−2000000000000
χ572-2-22-222-200-2202-20i2i2−i2−i2−i2−i2i2i22i−2i−2i2i02i−2i−2i2i0-22002-200i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2000000000000−222−22−2−22000000000000
χ582-2-22-222-200-2202-20i2i2−i2−i2−i2−i2i2i22i−2i−2i2i0−2i2i2i−2i02-200-2200i2−i2−i2i2−i2−i2i2i2i2i2−i2−i2000000000000−222−2−222−2000000000000
χ592-2-22-222-200-2202-20i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i02i−2i−2i2i02-200-2200i2−i2−i2i2−i2−i2i2i2i2i2−i2−i20000000000002−2−222−2−22000000000000
χ602-2-22-222-200-2202-20i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i0−2i2i2i−2i0-22002-200i2−i2−i2i2i2i2−i2−i2−i2−i2i2i20000000000002−2−22−222−2000000000000
χ612-2-22-222-200-2202-20−i2−i2i2i2i2i2−i2−i22i−2i−2i2i02i−2i−2i2i0-22002-200−i2i2i2−i2−i2−i2i2i2i2i2−i2−i20000000000002−2−22−222−2000000000000
χ622-2-22-222-200-2202-20−i2−i2i2i2i2i2−i2−i22i−2i−2i2i0−2i2i2i−2i02-200-2200−i2i2i2−i2i2i2−i2−i2−i2−i2i2i20000000000002−2−222−2−22000000000000
χ632-2-22-222-200-2202-20−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i02i−2i−2i2i02-200-2200−i2i2i2−i2i2i2−i2−i2−i2−i2i2i2000000000000−222−2−222−2000000000000
χ642-2-22-222-200-2202-20−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i0−2i2i2i−2i0-22002-200−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2000000000000−222−22−2−22000000000000
χ6544444444-4-4-4-4-4-4-4-40000000000004000040000000000000000000000000000000000000000000000000000
χ664444-4-4-4-44-400-400400000000000000000000000000000022−2222−2222−2222−2200000000000000000000000000000000
χ674444-4-4-4-44-400-4004000000000000000000000000000000−2222−2222−2222−222200000000000000000000000000000000
χ684444-4-4-4-4-4400400-44-44-44-44-400000000000000000000000000000000000000000000000000000000000000
χ694444-4-4-4-4-4400400-4-44-44-44-4400000000000000000000000000000000000000000000000000000000000000
χ7044-4-444-4-44400-400-44-44-4-44-4400000000000000000000000000000000000000000000000000000000000000
χ7144-4-444-4-44400-400-4-44-444-44-400000000000000000000000000000000000000000000000000000000000000
χ7244-4-444-4-4-4-40040040000000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000
χ7344-4-444-4-4-4-4004004000000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000
χ7444-4-4-4-4444-4444-4-4-400000000000040000-40000000000000000000000000000000000000000000000000000
χ754-44-44-44-400-440-4402i22i2−2i2−2i22i22i2−2i2−2i2000000000000000000−2i22i2−2i22i20000000000000000000000000000000000000000
χ764-44-44-44-400-440-440−2i2−2i22i22i2−2i2−2i22i22i20000000000000000002i2−2i22i2−2i20000000000000000000000000000000000000000
χ774-44-4-44-44000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000002i2−2i2002i2−2i200002-2-222-2-2200000000000000000000000000000000
χ784-44-4-44-44000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000−2i22i200−2i22i20000-222-2-222-200000000000000000000000000000000
χ794-44-4-44-4400000000−2i22i22i2−2i2−2i22i22i2−2i20000000000002i2−2i2002i2−2i20000-222-2-222-200000000000000000000000000000000
χ804-44-4-44-4400000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000−2i22i200−2i22i200002-2-222-2-2200000000000000000000000000000000
χ814-4-444-4-44000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000022−2200−22220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ824-4-444-4-44000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000−22220022−2200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ834-4-444-4-4400000000−2i22i22i2−2i22i2−2i2−2i22i200000000000022−2200−222200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ844-4-444-4-4400000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000−22220022−220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ854-4-44-444-4004-40-4402i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ864-4-44-444-4004-40-440−2i2−2i22i22i22i22i2−2i2−2i20000000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000

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