Finite Group Databasebeta

← Group #229421

Character table — Group #229421

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
χ311111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111
χ51111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111111-1-111-1-1-1-111
χ1711-11-1-1-11-111-1-1-1111111-1-1-1-1111-1-1ii−i−i-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
χ1811-11-1-1-11-111-1-1-1111111-1-1-1-1111-1-1ii−i−i-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
χ1911-11-1-1-11-111-1-1-1111111-1-1-1-1111-1-1−i−iii-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
χ2011-11-1-1-11-111-1-1-1111111-1-1-1-1111-1-1−i−iii-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
χ2111-11-1-1-11-111-1-1-1111111-1-1-1-11-1-111ii−i−i-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
χ2211-11-1-1-11-111-1-1-1111111-1-1-1-11-1-111ii−i−i-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
χ2311-11-1-1-11-111-1-1-1111111-1-1-1-11-1-111−i−iii-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
χ2411-11-1-1-11-111-1-1-1111111-1-1-1-11-1-111−i−iii-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
χ2511-11-1-1-11-111-1-1-111-1-1-1-11111111-1-1ii−i−i-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
χ2611-11-1-1-11-111-1-1-111-1-1-1-11111111-1-1ii−i−i-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
χ2711-11-1-1-11-111-1-1-111-1-1-1-11111111-1-1−i−iii-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
χ2811-11-1-1-11-111-1-1-111-1-1-1-11111111-1-1−i−iii-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
χ2911-11-1-1-11-111-1-1-111-1-1-1-111111-1-111ii−i−i-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
χ3011-11-1-1-11-111-1-1-111-1-1-1-111111-1-111ii−i−i-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
χ3111-11-1-1-11-111-1-1-111-1-1-1-111111-1-111−i−iii-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
χ3211-11-1-1-11-111-1-1-111-1-1-1-111111-1-111−i−iii-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
χ33222222222-22-2-222-222222222-200000000-200000000-2-2-2-200000000002222-2-2-2-20000000000000000000000
χ34222222222-22-2-222-222222222-200000000-200000000-2-2-2-20000000000-2-2-2-222220000000000000000000000
χ35222222222-22-2-222-2-2-2-2-2-2-2-2-2-200000000-2000000002222000000000022-2-2-2-2220000000000000000000000
χ36222222222-22-2-222-2-2-2-2-2-2-2-2-2-200000000-20000000022220000000000-2-22222-2-20000000000000000000000
χ3722222222-22-222-2-2200000000-222222222-222-2-222-2-2000000000000-2-200000000-2-200000000000000000000
χ3822222222-22-222-2-2200000000-22222-2-2-2-2-2-2-222-2-2220000000000002200000000-2-200000000000000000000
χ3922222222-22-222-2-2200000000-2-2-2-2-22222-2-2-222-2-222000000000000-2-2000000002200000000000000000000
χ4022222222-22-222-2-2200000000-2-2-2-2-2-2-2-2-2-222-2-222-2-200000000000022000000002200000000000000000000
χ4122-22-2-2-2222-2-2-22-2200000000-222-2-22i2i−2i−2i22i2i−2i−2i−2i−2i2i2i000000000000−2i2i00000000-2200000000000000000000
χ4222-22-2-2-2222-2-2-22-2200000000-222-2-2−2i−2i2i2i2−2i−2i2i2i2i2i−2i−2i0000000000002i−2i00000000-2200000000000000000000
χ4322-22-2-2-2222-2-2-22-2200000000-2-2-2222i2i−2i−2i2−2i−2i2i2i2i2i−2i−2i000000000000−2i2i000000002-200000000000000000000
χ4422-22-2-2-2222-2-2-22-2200000000-2-2-222−2i−2i2i2i22i2i−2i−2i−2i−2i2i2i0000000000002i−2i000000002-200000000000000000000
χ4522-22-2-2-22-2-2222-22-22222-2-2-2-2-200000000200000000-2-22200000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ4622-22-2-2-22-2-2222-22-22222-2-2-2-2-200000000200000000-2-2220000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ4722-22-2-2-22-2-2222-22-2-2-2-2-22222-20000000020000000022-2-200000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ4822-22-2-2-22-2-2222-22-2-2-2-2-22222-20000000020000000022-2-20000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ492-22-2-2-2220202-200-222−2−222−2−202i−2i2i−2i2i−2i2i−2i02-2002-2002−22−222−2−222−2−2000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ502-22-2-2-2220202-200-222−2−222−2−202i−2i2i−2i−2i2i−2i2i0-2200-22002−22−2−2−222−2−222000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ512-22-2-2-2220202-200-222−2−222−2−20−2i2i−2i2i2i−2i2i−2i0-2200-22002−22−2−2−222−2−222000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ522-22-2-2-2220202-200-222−2−222−2−20−2i2i−2i2i−2i2i−2i2i02-2002-2002−22−222−2−222−2−2000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ532-22-2-2-2220202-200-2−2−222−2−22202i−2i2i−2i2i−2i2i−2i02-2002-200−22−22−2−222−2−222000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ542-22-2-2-2220202-200-2−2−222−2−22202i−2i2i−2i−2i2i−2i2i0-2200-2200−22−2222−2−222−2−2000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ552-22-2-2-2220202-200-2−2−222−2−2220−2i2i−2i2i2i−2i2i−2i0-2200-2200−22−2222−2−222−2−2000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ562-22-2-2-2220202-200-2−2−222−2−2220−2i2i−2i2i−2i2i−2i2i02-2002-200−22−22−2−222−2−222000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ572-2-2-222-22020-2200-222−2−2−2−22202i−2i−2i2i2-2-220−2i2i002i−2i002−2−22−i2−i2i2i2i2i2−i2−i20000000000002−2−22i2−i2−i2i2000000000000
χ582-2-2-222-22020-2200-222−2−2−2−22202i−2i−2i2i-222-202i−2i00−2i2i002−2−22i2i2−i2−i2−i2−i2i2i2000000000000−222−2i2−i2−i2i2000000000000
χ592-2-2-222-22020-2200-222−2−2−2−2220−2i2i2i−2i2-2-2202i−2i00−2i2i002−2−22i2i2−i2−i2−i2−i2i2i20000000000002−2−22−i2i2i2−i2000000000000
χ602-2-2-222-22020-2200-222−2−2−2−2220−2i2i2i−2i-222-20−2i2i002i−2i002−2−22−i2−i2i2i2i2i2−i2−i2000000000000−222−2−i2i2i2−i2000000000000
χ612-2-2-222-22020-2200-2−2−22222−2−202i−2i−2i2i2-2-220−2i2i002i−2i00−222−2i2i2−i2−i2−i2−i2i2i2000000000000−222−2−i2i2i2−i2000000000000
χ622-2-2-222-22020-2200-2−2−22222−2−202i−2i−2i2i-222-202i−2i00−2i2i00−222−2−i2−i2i2i2i2i2−i2−i20000000000002−2−22−i2i2i2−i2000000000000
χ632-2-2-222-22020-2200-2−2−22222−2−20−2i2i2i−2i2-2-2202i−2i00−2i2i00−222−2−i2−i2i2i2i2i2−i2−i2000000000000−222−2i2−i2−i2i2000000000000
χ642-2-2-222-22020-2200-2−2−22222−2−20−2i2i2i−2i-222-20−2i2i002i−2i00−222−2i2i2−i2−i2−i2−i2i2i20000000000002−2−22i2−i2−i2i2000000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000000040000000000000000000000000000000000000000000000000000
χ66444-4-44-4-440-400-44000000000000000000000000000000022−2222−2222−2222−2200000000000000000000000000000000
χ67444-4-44-4-440-400-440000000000000000000000000000000−2222−2222−2222−222200000000000000000000000000000000
χ68444-4-44-4-4-404004-404-44-44-44-400000000000000000000000000000000000000000000000000000000000000
χ69444-4-44-4-4-404004-40-44-44-44-4400000000000000000000000000000000000000000000000000000000000000
χ7044-44-4-4-444-4-4444-4-400000000400000000-40000000000000000000000000000000000000000000000000000
χ7144-4-44-44-440400-4-404-44-4-44-4400000000000000000000000000000000000000000000000000000000000000
χ7244-4-44-44-440400-4-40-44-444-44-400000000000000000000000000000000000000000000000000000000000000
χ7344-4-44-44-4-40-4004400000000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000
χ7444-4-44-44-4-40-400440000000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000
χ754-4444-4-4-40000000022−22−222222−22−222200000000000022−220022−2200002-2-222-2-2200000000000000000000000000000000
χ764-4444-4-4-40000000022−22−222222−22−2222000000000000−222200−22220000-222-2-222-200000000000000000000000000000000
χ774-4444-4-4-400000000−222222−22−222222−2200000000000022−220022−220000-222-2-222-200000000000000000000000000000000
χ784-4444-4-4-400000000−222222−22−222222−22000000000000−222200−222200002-2-222-2-2200000000000000000000000000000000
χ794-44-4-4-4440-40-440042222−22−222222−22−22000000000000000000−2222−22220000000000000000000000000000000000000000
χ804-44-4-4-4440-40-44004−22−222222−22−22222200000000000000000022−2222−220000000000000000000000000000000000000000
χ814-4-44-444-40000000022−22−2222−222222−220000000000002i2−2i200−2i22i200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ824-4-44-444-40000000022−22−2222−222222−22000000000000−2i22i2002i2−2i20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ834-4-44-444-400000000−222222−2222−22−22220000000000002i2−2i200−2i22i20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ844-4-44-444-400000000−222222−2222−22−2222000000000000−2i22i2002i2−2i200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ854-4-4-444-440-404-40042222−22−22−22−222222000000000000000000−222222−220000000000000000000000000000000000000000
χ864-4-4-444-440-404-4004−22−2222222222−22−2200000000000000000022−22−22220000000000000000000000000000000000000000

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