Finite Group Databasebeta

← Group #229403

Character table — Group #229403

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888844444444448888888888888888888822444444444488888888222244448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ51111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-1-1-11111-1-11111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-111-1-1-1-111
χ17111-11-1-1-11-1-1-11-1111111-1-1-1-1111-1-1ii−i−i-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1i−ii−ii−ii−ii−iii−i−i11-1-11-11-1i−ii−i1-11-1
χ18111-11-1-1-11-1-1-11-1111111-1-1-1-1111-1-1ii−i−i-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1i−i−ii−ii−ii−iiii−i−i11-1-1-11-11−ii−ii-11-11
χ19111-11-1-1-11-1-1-11-1111111-1-1-1-1111-1-1−i−iii-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−iii−ii−ii−ii−i−i−iii11-1-1-11-11i−ii−i-11-11
χ20111-11-1-1-11-1-1-11-1111111-1-1-1-1111-1-1−i−iii-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−ii−ii−ii−ii−ii−i−iii11-1-11-11-1−ii−ii1-11-1
χ21111-11-1-1-11-1-1-11-1111111-1-1-1-11-1-111ii−i−i-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11i−ii−ii−ii−ii−iii−i−i-1-1111-11-1−ii−ii-11-11
χ22111-11-1-1-11-1-1-11-1111111-1-1-1-11-1-111ii−i−i-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11i−i−ii−ii−ii−iiii−i−i-1-111-11-11i−ii−i1-11-1
χ23111-11-1-1-11-1-1-11-1111111-1-1-1-11-1-111−i−iii-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11−iii−ii−ii−ii−i−i−iii-1-111-11-11−ii−ii1-11-1
χ24111-11-1-1-11-1-1-11-1111111-1-1-1-11-1-111−i−iii-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11−ii−ii−ii−ii−ii−i−iii-1-1111-11-1i−ii−i-11-11
χ25111-11-1-1-11-1-1-11-111-1-1-1-11111111-1-1ii−i−i-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1i−ii−i−iii−i−ii−i−iii-1-1111-1-11i−i−ii1-1-11
χ26111-11-1-1-11-1-1-11-111-1-1-1-11111111-1-1ii−i−i-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1i−i−iii−i−iii−i−i−iii-1-111-111-1−iii−i-111-1
χ27111-11-1-1-11-1-1-11-111-1-1-1-11111111-1-1−i−iii-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1−iii−i−iii−i−iiii−i−i-1-111-111-1i−i−ii-111-1
χ28111-11-1-1-11-1-1-11-111-1-1-1-11111111-1-1−i−iii-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1−ii−iii−i−iii−iii−i−i-1-1111-1-11−iii−i1-1-11
χ29111-11-1-1-11-1-1-11-111-1-1-1-111111-1-111ii−i−i-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-11i−ii−i−iii−i−ii−i−iii11-1-11-1-11−iii−i-111-1
χ30111-11-1-1-11-1-1-11-111-1-1-1-111111-1-111ii−i−i-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-11i−i−iii−i−iii−i−i−iii11-1-1-111-1i−i−ii1-1-11
χ31111-11-1-1-11-1-1-11-111-1-1-1-111111-1-111−i−iii-1-1-111iiii−i−i−i−i−i−i−i−iiiii-11−iii−i−iii−i−iiii−i−i11-1-1-111-1−iii−i1-1-11
χ32111-11-1-1-11-1-1-11-111-1-1-1-111111-1-111−i−iii-1-1-111iiii−i−i−i−i−i−i−i−iiiii-11−ii−iii−i−iii−iii−i−i11-1-11-1-11i−i−ii-111-1
χ33222222222-222-2-2-2200000000-222222222-2000022-2-222-2-200000000-2-2-2-20000000000000000000000000000
χ34222222222-222-2-2-2200000000-22222-2-2-2-2-20000-2-222-2-22200000000-2-2220000000000000000000000000000
χ35222222222-222-2-2-2200000000-2-2-2-2-22222-20000-2-222-2-2220000000022-2-20000000000000000000000000000
χ36222222222-222-2-2-2200000000-2-2-2-2-2-2-2-2-2-2000022-2-222-2-20000000022220000000000000000000000000000
χ3722222222-22-2-2222-222222222-200000000-2-2-2-2-2000000000000000000002222-2-2-2-200000000000000000000
χ3822222222-22-2-2222-222222222-200000000-2-2-2-2-200000000000000000000-2-2-2-2222200000000000000000000
χ3922222222-22-2-2222-2-2-2-2-2-2-2-2-2-200000000-222220000000000000000000022-2-2-2-22200000000000000000000
χ4022222222-22-2-2222-2-2-2-2-2-2-2-2-2-200000000-2222200000000000000000000-2-22222-2-200000000000000000000
χ41222-22-2-2-222-2-2-22-2200000000-222-2-22i2i−2i−2i200002i2i−2i−2i−2i−2i2i2i00000000-22−2i2i0000000000000000000000000000
χ42222-22-2-2-222-2-2-22-2200000000-222-2-2−2i−2i2i2i20000−2i−2i2i2i2i2i−2i−2i00000000-222i−2i0000000000000000000000000000
χ43222-22-2-2-222-2-2-22-2200000000-2-2-2222i2i−2i−2i20000−2i−2i2i2i2i2i−2i−2i000000002-2−2i2i0000000000000000000000000000
χ44222-22-2-2-222-2-2-22-2200000000-2-2-222−2i−2i2i2i200002i2i−2i−2i−2i−2i2i2i000000002-22i−2i0000000000000000000000000000
χ45222-22-2-2-2-2-2222-22-22222-2-2-2-2-2000000002-2-222000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ46222-22-2-2-2-2-2222-22-22222-2-2-2-2-2000000002-2-22200000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ47222-22-2-2-2-2-2222-22-2-2-2-2-22222-200000000222-2-2000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ48222-22-2-2-2-2-2222-22-2-2-2-2-22222-200000000222-2-200000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ4922-22-2-2-22202-2000-222−2−222−2−202i−2i2i−2i2i−2i2i−2i02−22−22-2002-20022−2−222−2−2000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ5022-22-2-2-22202-2000-222−2−222−2−202i−2i2i−2i−2i2i−2i2i02−22−2-2200-2200−2−222−2−222000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ5122-22-2-2-22202-2000-222−2−222−2−20−2i2i−2i2i2i−2i2i−2i02−22−2-2200-2200−2−222−2−222000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ5222-22-2-2-22202-2000-222−2−222−2−20−2i2i−2i2i−2i2i−2i2i02−22−22-2002-20022−2−222−2−2000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ5322-22-2-2-22202-2000-2−2−222−2−22202i−2i2i−2i2i−2i2i−2i0−22−222-2002-200−2−222−2−222000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ5422-22-2-2-22202-2000-2−2−222−2−22202i−2i2i−2i−2i2i−2i2i0−22−22-2200-220022−2−222−2−2000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ5522-22-2-2-22202-2000-2−2−222−2−2220−2i2i−2i2i2i−2i2i−2i0−22−22-2200-220022−2−222−2−2000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ5622-22-2-2-22202-2000-2−2−222−2−2220−2i2i−2i2i−2i2i−2i2i0−22−222-2002-200−2−222−2−222000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ5722-2-2-222-220-22000-222−2−2−2−22202i−2i−2i2i2-2-2202−2−22−2i2i002i−2i00−i2−i2i2i2i2i2−i2−i20000000000002−2−22i2−i2−i2i2000000000000
χ5822-2-2-222-220-22000-222−2−2−2−22202i−2i−2i2i-222-202−2−222i−2i00−2i2i00i2i2−i2−i2−i2−i2i2i2000000000000−222−2i2−i2−i2i2000000000000
χ5922-2-2-222-220-22000-222−2−2−2−2220−2i2i2i−2i2-2-2202−2−222i−2i00−2i2i00i2i2−i2−i2−i2−i2i2i20000000000002−2−22−i2i2i2−i2000000000000
χ6022-2-2-222-220-22000-222−2−2−2−2220−2i2i2i−2i-222-202−2−22−2i2i002i−2i00−i2−i2i2i2i2i2−i2−i2000000000000−222−2−i2i2i2−i2000000000000
χ6122-2-2-222-220-22000-2−2−22222−2−202i−2i−2i2i2-2-220−222−2−2i2i002i−2i00i2i2−i2−i2−i2−i2i2i2000000000000−222−2−i2i2i2−i2000000000000
χ6222-2-2-222-220-22000-2−2−22222−2−202i−2i−2i2i-222-20−222−22i−2i00−2i2i00−i2−i2i2i2i2i2−i2−i20000000000002−2−22−i2i2i2−i2000000000000
χ6322-2-2-222-220-22000-2−2−22222−2−20−2i2i2i−2i2-2-220−222−22i−2i00−2i2i00−i2−i2i2i2i2i2−i2−i2000000000000−222−2i2−i2−i2i2000000000000
χ6422-2-2-222-220-22000-2−2−22222−2−20−2i2i2i−2i-222-20−222−2−2i2i002i−2i00i2i2−i2−i2−i2−i2i2i20000000000002−2−22i2−i2−i2i2000000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000000040000000000000000000000000000000000000000000000000000
χ66444-44-4-4-4-4444-44-4-400000000400000000-40000000000000000000000000000000000000000000000000000
χ6744-44-4-4-44-40-4400042222−22−222222−22−220000000000−2222−2222000000000000000000000000000000000000000000000000
χ6844-44-4-4-44-40-440004−22−222222−22−222222000000000022−2222−22000000000000000000000000000000000000000000000000
χ6944-4-4-444-4-404-400042222−22−22−22−2222220000000000−222222−22000000000000000000000000000000000000000000000000
χ7044-4-4-444-4-404-40004−22−2222222222−22−22000000000022−22−2222000000000000000000000000000000000000000000000000
χ714-444-44-4-40000000022−2222−2222−2222−2200000000000000002i2−2i2002i2−2i22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ724-444-44-4-40000000022−2222−2222−2222−220000000000000000−2i22i200−2i22i2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ734-444-44-4-400000000−2222−2222−2222−222200000000000000002i2−2i2002i2−2i2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ744-444-44-4-400000000−2222−2222−2222−22220000000000000000−2i22i200−2i22i22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ754-44-4-4-4440000000022−2222−22−2222−2222000000000000000022−2200−22222-22-2-22-2200000000000000000000000000000000
χ764-44-4-4-4440000000022−2222−22−2222−22220000000000000000−22220022−22-22-222-22-200000000000000000000000000000000
χ774-44-4-4-44400000000−2222−222222−2222−22000000000000000022−2200−2222-22-222-22-200000000000000000000000000000000
χ784-44-4-4-44400000000−2222−222222−2222−220000000000000000−22220022−222-22-2-22-2200000000000000000000000000000000
χ794-4-444-44-404004-4-400000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ804-4-444-44-404004-4-40000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ814-4-444-44-40-400-44404-4-444-4-4400000000000000000000000000000000000000000000000000000000000000
χ824-4-444-44-40-400-4440-444-4-444-400000000000000000000000000000000000000000000000000000000000000
χ834-4-4-444-440400-4-4404-4-44-444-400000000000000000000000000000000000000000000000000000000000000
χ844-4-4-444-440400-4-440-444-44-4-4400000000000000000000000000000000000000000000000000000000000000
χ854-4-4-444-440-40044-4000000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000
χ864-4-4-444-440-40044-40000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000

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