Finite Group Databasebeta

← Group #229423

Character table — Group #229423

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888822224444448888888888888888888844444444444488888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-111
χ1711-11-11-1-1-1-1-1111-111111-1-1-1-111-1-1ii−i−i1-111-1-1iiii−i−i−i−iiiii−i−i−i−ii−i1-1i−ii−ii−ii−iii−i−i11-1-11-11-1i−ii−i1-11-1
χ1811-11-11-1-1-1-1-1111-111111-1-1-1-111-1-1ii−i−i1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−ii1-1−ii−iii−i−iiii−i−i11-1-1-11-11−ii−ii-11-11
χ1911-11-11-1-1-1-1-1111-111111-1-1-1-111-1-1−i−iii1-111-1-1−i−i−i−iiiii−i−i−i−iiiiii−i1-1i−ii−i−iii−i−i−iii11-1-1-11-11i−ii−i-11-11
χ2011-11-11-1-1-1-1-1111-111111-1-1-1-111-1-1−i−iii1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−ii1-1−ii−ii−ii−ii−i−iii11-1-11-11-1−ii−ii1-11-1
χ2111-11-11-1-1-1-1-1111-111111-1-1-1-1-1-111ii−i−i1-111-1-1−i−i−i−iiiii−i−i−i−iiiiii−i-11i−ii−ii−ii−iii−i−i-1-1111-11-1−ii−ii-11-11
χ2211-11-11-1-1-1-1-1111-111111-1-1-1-1-1-111ii−i−i1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−ii-11−ii−iii−i−iiii−i−i-1-111-11-11i−ii−i1-11-1
χ2311-11-11-1-1-1-1-1111-111111-1-1-1-1-1-111−i−iii1-111-1-1iiii−i−i−i−iiiii−i−i−i−ii−i-11i−ii−i−iii−i−i−iii-1-111-11-11−ii−ii1-11-1
χ2411-11-11-1-1-1-1-1111-111111-1-1-1-1-1-111−i−iii1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−ii-11−ii−ii−ii−ii−i−iii-1-1111-11-1i−ii−i-11-11
χ2511-11-11-1-1-1-1-1111-11-1-1-1-1111111-1-1ii−i−i1-1-1-111iiii−i−i−i−i−i−i−i−iiiiii−i1-1−ii−iii−ii−i−i−iii-1-111-111-1−iii−i1-1-11
χ2611-11-11-1-1-1-1-1111-11-1-1-1-1111111-1-1ii−i−i1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−ii1-1i−ii−ii−i−ii−i−iii-1-1111-1-11i−i−ii-111-1
χ2711-11-11-1-1-1-1-1111-11-1-1-1-1111111-1-1−i−iii1-1-1-111−i−i−i−iiiiiiiii−i−i−i−ii−i1-1−ii−ii−iii−iii−i−i-1-1111-1-11−iii−i-111-1
χ2811-11-11-1-1-1-1-1111-11-1-1-1-1111111-1-1−i−iii1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−ii1-1i−ii−i−ii−iiii−i−i-1-111-111-1i−i−ii1-1-11
χ2911-11-11-1-1-1-1-1111-11-1-1-1-11111-1-111ii−i−i1-1-1-111−i−i−i−iiiiiiiii−i−i−i−ii−i-11−ii−iii−ii−i−i−iii11-1-1-111-1i−i−ii-111-1
χ3011-11-11-1-1-1-1-1111-11-1-1-1-11111-1-111ii−i−i1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−ii-11i−ii−ii−i−ii−i−iii11-1-11-1-11−iii−i1-1-11
χ3111-11-11-1-1-1-1-1111-11-1-1-1-11111-1-111−i−iii1-1-1-111iiii−i−i−i−i−i−i−i−iiiiii−i-11−ii−ii−iii−iii−i−i11-1-11-1-11i−i−ii1-1-11
χ3211-11-11-1-1-1-1-1111-11-1-1-1-11111-1-111−i−iii1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−ii-11i−ii−i−ii−iiii−i−i11-1-1-111-1−iii−i-111-1
χ33222222222-2-22-2-2222222222200000000-2-2-2-2-2-20000000000000000220022-2-200-2-200000000000000000000
χ34222222222-2-22-2-2222222222200000000-2-2-2-2-2-20000000000000000-2-200-2-222002200000000000000000000
χ35222222222-2-22-2-222-2-2-2-2-2-2-2-200000000-2-2222200000000000000002200-2-22200-2-200000000000000000000
χ36222222222-2-22-2-222-2-2-2-2-2-2-2-200000000-2-222220000000000000000-2-20022-2-2002200000000000000000000
χ3722222222-222-222-2-20000000022222222-2-2000022-2-222-2-20000000000-2-20000-2-20000000000000000000000
χ3822222222-222-222-2-2000000002222-2-2-2-2-2-20000-2-222-2-2220000000000-2-20000220000000000000000000000
χ3922222222-222-222-2-200000000-2-2-2-22222-2-20000-2-222-2-2220000000000220000-2-20000000000000000000000
χ4022222222-222-222-2-200000000-2-2-2-2-2-2-2-2-2-2000022-2-222-2-20000000000220000220000000000000000000000
χ41222-2-2-2-2202-202-200i2i2−i2−i2i2i2−i2−i22-22-22i−2i2i−2i00i2−i2i2−i22i−2i002i−2i0022−2−222−2−20000000000002−22−2i2−i2i2−i2000000000000
χ42222-2-2-2-2202-202-200i2i2−i2−i2i2i2−i2−i22-22-2−2i2i−2i2i00i2−i2i2−i2−2i2i00−2i2i00−2−222−2−222000000000000−22−22i2−i2i2−i2000000000000
χ43222-2-2-2-2202-202-200i2i2−i2−i2i2i2−i2−i2-22-222i−2i2i−2i00i2−i2i2−i2−2i2i00−2i2i00−2−222−2−2220000000000002−22−2−i2i2−i2i2000000000000
χ44222-2-2-2-2202-202-200i2i2−i2−i2i2i2−i2−i2-22-22−2i2i−2i2i00i2−i2i2−i22i−2i002i−2i0022−2−222−2−2000000000000−22−22−i2i2−i2i2000000000000
χ45222-2-2-2-2202-202-200−i2−i2i2i2−i2−i2i2i22-22-22i−2i2i−2i00−i2i2−i2i22i−2i002i−2i00−2−222−2−222000000000000−22−22−i2i2−i2i2000000000000
χ46222-2-2-2-2202-202-200−i2−i2i2i2−i2−i2i2i22-22-2−2i2i−2i2i00−i2i2−i2i2−2i2i00−2i2i0022−2−222−2−20000000000002−22−2−i2i2−i2i2000000000000
χ47222-2-2-2-2202-202-200−i2−i2i2i2−i2−i2i2i2-22-222i−2i2i−2i00−i2i2−i2i2−2i2i00−2i2i0022−2−222−2−2000000000000−22−22i2−i2i2−i2000000000000
χ48222-2-2-2-2202-202-200−i2−i2i2i2−i2−i2i2i2-22-22−2i2i−2i2i00−i2i2−i2i22i−2i002i−2i00−2−222−2−2220000000000002−22−2i2−i2i2−i2000000000000
χ4922-22-22-2-22-2-2-2222-20000000022-2-22i2i−2i−2i-2200002i2i−2i−2i−2i−2i2i2i0000000000-220000−2i2i0000000000000000000000
χ5022-22-22-2-22-2-2-2222-20000000022-2-2−2i−2i2i2i-220000−2i−2i2i2i2i2i−2i−2i0000000000-2200002i−2i0000000000000000000000
χ5122-22-22-2-22-2-2-2222-200000000-2-2222i2i−2i−2i-220000−2i−2i2i2i2i2i−2i−2i00000000002-20000−2i2i0000000000000000000000
χ5222-22-22-2-22-2-2-2222-200000000-2-222−2i−2i2i2i-2200002i2i−2i−2i−2i−2i2i2i00000000002-200002i−2i0000000000000000000000
χ5322-22-22-2-2-2222-2-2-222222-2-2-2-200000000-22-2-22200000000000000002i−2i002i−2i−2i2i00−2i2i00000000000000000000
χ5422-22-22-2-2-2222-2-2-222222-2-2-2-200000000-22-2-2220000000000000000−2i2i00−2i2i2i−2i002i−2i00000000000000000000
χ5522-22-22-2-2-2222-2-2-22-2-2-2-2222200000000-2222-2-200000000000000002i−2i00−2i2i2i−2i00−2i2i00000000000000000000
χ5622-22-22-2-2-2222-2-2-22-2-2-2-2222200000000-2222-2-20000000000000000−2i2i002i−2i−2i2i002i−2i00000000000000000000
χ5722-2-22-22-20-2202-200i2i2−i2−i2−i2−i2i2i22-2-222-2-2200i2−i2−i2i22-200-2200−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ5822-2-22-22-20-2202-200i2i2−i2−i2−i2−i2i2i22-2-22-222-200i2−i2−i2i2-22002-200i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ5922-2-22-22-20-2202-200i2i2−i2−i2−i2−i2i2i2-222-22-2-2200i2−i2−i2i2-22002-200i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ6022-2-22-22-20-2202-200i2i2−i2−i2−i2−i2i2i2-222-2-222-200i2−i2−i2i22-200-2200−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ6122-2-22-22-20-2202-200−i2−i2i2i2i2i2−i2−i22-2-222-2-2200−i2i2i2−i22-200-2200i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ6222-2-22-22-20-2202-200−i2−i2i2i2i2i2−i2−i22-2-22-222-200−i2i2i2−i2-22002-200−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ6322-2-22-22-20-2202-200−i2−i2i2i2i2i2−i2−i2-222-22-2-2200−i2i2i2−i2-22002-200−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ6422-2-22-22-20-2202-200−i2−i2i2i2i2i2−i2−i2-222-2-222-200−i2i2i2−i22-200-2200i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ6544444444-4-4-4-4-4-4-4-40000000000000000440000000000000000000000000000000000000000000000000000
χ66444-4-4-4-440-440-44002i22i2−2i2−2i22i22i2−2i2−2i20000000000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ67444-4-4-4-440-440-4400−2i2−2i22i22i2−2i2−2i22i22i200000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ6844-44-44-4-4444-4-4-44-400000000000000004-40000000000000000000000000000000000000000000000000000
χ6944-4-44-44-404-40-44002i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ7044-4-44-44-404-40-4400−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ714-444-4-44-4400-400-440000000000000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000
χ724-444-4-44-4400-400-44000000000000000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000
χ734-444-4-44-4-4004004-44i−4i4i−4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ744-444-4-44-4-4004004-4−4i4i−4i4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ754-44-444-4-40000000022−22−222222−22−222200000000000000002i2−2i2002i2−2i22i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ764-44-444-4-40000000022−22−222222−22−22220000000000000000−2i22i200−2i22i2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ774-44-444-4-400000000−222222−22−222222−2200000000000000002i2−2i2002i2−2i2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ784-44-444-4-400000000−222222−22−222222−220000000000000000−2i22i200−2i22i22i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ794-4-444-4-44400400-4-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ804-4-444-4-44400400-4-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ814-4-444-4-44-400-4004400000000000000000000000000000022−2222−22−2222−222200000000000000000000000000000000
χ824-4-444-4-44-400-40044000000000000000000000000000000−2222−222222−2222−2200000000000000000000000000000000
χ834-4-4-4-44440000000022−22−2222−222222−22000000000000000022−2200−22222-2-22-222-200000000000000000000000000000000
χ844-4-4-4-44440000000022−22−2222−222222−220000000000000000−22220022−22-222-22-2-2200000000000000000000000000000000
χ854-4-4-4-444400000000−222222−2222−22−2222000000000000000022−2200−2222-222-22-2-2200000000000000000000000000000000
χ864-4-4-4-444400000000−222222−2222−22−22220000000000000000−22220022−222-2-22-222-200000000000000000000000000000000

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