Finite Group Databasebeta

← Group #231571

Character table — Group #231571

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888844444444448888888888888888888844444444444488888888222244448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111
χ51111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-111-1-1-1-1
χ61111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111
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
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111
χ17111-1-1-1-111111-1-1-1-11111-1-1-1-1-1ii−i−iii−i−i111-1-11111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1i−ii−i
χ18111-1-1-1-111111-1-1-1-11111-1-1-1-1-1ii−i−iii−i−i111-1-11111-1-1-1-11111-1-1-1-1i−ii−i−i−iii−i−iiiii−i−iii−i−i-11-11-11-11−ii−ii
χ19111-1-1-1-111111-1-1-1-11111-1-1-1-1-1ii−i−i−i−iii111-1-1-1-1-1-11111-1-1-1-11111i−i−iiii−i−iii−i−iii−i−i−i−iii1-1-111-1-11−ii−ii
χ20111-1-1-1-111111-1-1-1-11111-1-1-1-1-1ii−i−i−i−iii111-1-1-1-1-1-11111-1-1-1-11111i−i−ii−i−iii−i−iiiii−i−i−i−iii-111-1-111-1i−ii−i
χ21111-1-1-1-111111-1-1-1-11111-1-1-1-1-1−i−iiiii−i−i111-1-1-1-1-1-11111-1-1-1-11111−iii−iii−i−iii−i−i−i−iiiii−i−i-111-1-111-1−ii−ii
χ22111-1-1-1-111111-1-1-1-11111-1-1-1-1-1−i−iiiii−i−i111-1-1-1-1-1-11111-1-1-1-11111−iii−i−i−iii−i−iii−i−iiiii−i−i1-1-111-1-11i−ii−i
χ23111-1-1-1-111111-1-1-1-11111-1-1-1-1-1−i−iii−i−iii111-1-11111-1-1-1-11111-1-1-1-1−ii−iiii−i−iii−i−i−i−iii−i−iii-11-11-11-11i−ii−i
χ24111-1-1-1-111111-1-1-1-11111-1-1-1-1-1−i−iii−i−iii111-1-11111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1−ii−ii
χ25111-1-1-1-111111-1-1-1-1-1-1-1-11111-1ii−i−iii−i−i1-1-1111111-1-1-1-1-1-1-1-11111i−ii−iii−i−i−i−iii−i−iii−i−iii1-11-1-11-11i−i−ii
χ26111-1-1-1-111111-1-1-1-1-1-1-1-11111-1ii−i−iii−i−i1-1-1111111-1-1-1-1-1-1-1-11111i−ii−i−i−iiiii−i−i−i−iii−i−iii-11-111-11-1−iii−i
χ27111-1-1-1-111111-1-1-1-1-1-1-1-11111-1ii−i−i−i−iii1-1-111-1-1-1-111111111-1-1-1-1i−i−iiii−i−i−i−iii−i−iiiii−i−i1-1-11-111-1−iii−i
χ28111-1-1-1-111111-1-1-1-1-1-1-1-11111-1ii−i−i−i−iii1-1-111-1-1-1-111111111-1-1-1-1i−i−ii−i−iiiii−i−i−i−iiiii−i−i-111-11-1-11i−i−ii
χ29111-1-1-1-111111-1-1-1-1-1-1-1-11111-1−i−iiiii−i−i1-1-111-1-1-1-111111111-1-1-1-1−iii−iii−i−i−i−iiiii−i−i−i−iii-111-11-1-11−iii−i
χ30111-1-1-1-111111-1-1-1-1-1-1-1-11111-1−i−iiiii−i−i1-1-111-1-1-1-111111111-1-1-1-1−iii−i−i−iiiii−i−iii−i−i−i−iii1-1-11-111-1i−i−ii
χ31111-1-1-1-111111-1-1-1-1-1-1-1-11111-1−i−iii−i−iii1-1-1111111-1-1-1-1-1-1-1-11111−ii−iiii−i−i−i−iiiii−i−iii−i−i-11-111-11-1i−i−ii
χ32111-1-1-1-111111-1-1-1-1-1-1-1-11111-1−i−iii−i−iii1-1-1111111-1-1-1-1-1-1-1-11111−ii−ii−i−iiiii−i−iii−i−iii−i−i1-11-1-11-11−iii−i
χ332222222222-2-222-2-200000000-222222222-2000022-2-222-2-200000000-2-2-2-20000000000000000000000000000
χ342222222222-2-222-2-200000000-22222-2-2-2-2-20000-2-222-2-22200000000-2-2220000000000000000000000000000
χ352222222222-2-222-2-200000000-2-2-2-2-22222-20000-2-222-2-2220000000022-2-20000000000000000000000000000
χ362222222222-2-222-2-200000000-2-2-2-2-2-2-2-2-2-2000022-2-222-2-20000000022220000000000000000000000000000
χ3722222222-2-222-2-22222222222-200000000-2-2-2-2-2000000000000000000002-22-22-22-200000000000000000000
χ3822222222-2-222-2-22222222222-200000000-2-2-2-2-200000000000000000000-22-22-22-2200000000000000000000
χ3922222222-2-222-2-222-2-2-2-2-2-2-2-2-200000000-22222000000000000000000002-22-2-22-2200000000000000000000
χ4022222222-2-222-2-222-2-2-2-2-2-2-2-2-200000000-2222200000000000000000000-22-222-22-200000000000000000000
χ41222-2-2-2-2222-2-2-2-2220000000022i2i−2i−2i2i2i−2i−2i-2000022-2-2-2-22200000000−2i2i−2i2i0000000000000000000000000000
χ42222-2-2-2-2222-2-2-2-2220000000022i2i−2i−2i−2i−2i2i2i-20000-2-22222-2-200000000−2i2i2i−2i0000000000000000000000000000
χ43222-2-2-2-2222-2-2-2-222000000002−2i−2i2i2i2i2i−2i−2i-20000-2-22222-2-2000000002i−2i−2i2i0000000000000000000000000000
χ44222-2-2-2-2222-2-2-2-222000000002−2i−2i2i2i−2i−2i2i2i-2000022-2-2-2-222000000002i−2i2i−2i0000000000000000000000000000
χ45222-2-2-2-22-2-22222-2-22222-2-2-2-2200000000-2-2-222000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ46222-2-2-2-22-2-22222-2-22222-2-2-2-2200000000-2-2-22200000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ47222-2-2-2-22-2-22222-2-2-2-2-2-22222200000000-222-2-2000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ48222-2-2-2-22-2-22222-2-2-2-2-2-22222200000000-222-2-200000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ4922-222-2-2-22-2002-200i2i2−i2−i2i2i2−i2−i202-22-22-22-20i2−i2i2−i22-2002-200i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ5022-222-2-2-22-2002-200i2i2−i2−i2i2i2−i2−i202-22-2-22-220i2−i2i2−i2-2200-2200−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ5122-222-2-2-22-2002-200i2i2−i2−i2i2i2−i2−i20-22-222-22-20i2−i2i2−i2-2200-2200−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ5222-222-2-2-22-2002-200i2i2−i2−i2i2i2−i2−i20-22-22-22-220i2−i2i2−i22-2002-200i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ5322-222-2-2-22-2002-200−i2−i2i2i2−i2−i2i2i202-22-22-22-20−i2i2−i2i22-2002-200−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ5422-222-2-2-22-2002-200−i2−i2i2i2−i2−i2i2i202-22-2-22-220−i2i2−i2i2-2200-2200i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ5522-222-2-2-22-2002-200−i2−i2i2i2−i2−i2i2i20-22-222-22-20−i2i2−i2i2-2200-2200i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ5622-222-2-2-22-2002-200−i2−i2i2i2−i2−i2i2i20-22-22-22-220−i2i2−i2i22-2002-200−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ5722-2-2-222-22-200-2200i2i2−i2−i2−i2−i2i2i202i−2i−2i2i2i−2i−2i2i0i2−i2−i2i22-200-2200i2i2−i2−i2−i2−i2i2i2000000000000−222−2−222−2000000000000
χ5822-2-2-222-22-200-2200i2i2−i2−i2−i2−i2i2i202i−2i−2i2i−2i2i2i−2i0i2−i2−i2i2-22002-200−i2−i2i2i2i2i2−i2−i2000000000000−222−22−2−22000000000000
χ5922-2-2-222-22-200-2200i2i2−i2−i2−i2−i2i2i20−2i2i2i−2i2i−2i−2i2i0i2−i2−i2i2-22002-200−i2−i2i2i2i2i2−i2−i20000000000002−2−22−222−2000000000000
χ6022-2-2-222-22-200-2200i2i2−i2−i2−i2−i2i2i20−2i2i2i−2i−2i2i2i−2i0i2−i2−i2i22-200-2200i2i2−i2−i2−i2−i2i2i20000000000002−2−222−2−22000000000000
χ6122-2-2-222-22-200-2200−i2−i2i2i2i2i2−i2−i202i−2i−2i2i2i−2i−2i2i0−i2i2i2−i22-200-2200−i2−i2i2i2i2i2−i2−i20000000000002−2−222−2−22000000000000
χ6222-2-2-222-22-200-2200−i2−i2i2i2i2i2−i2−i202i−2i−2i2i−2i2i2i−2i0−i2i2i2−i2-22002-200i2i2−i2−i2−i2−i2i2i20000000000002−2−22−222−2000000000000
χ6322-2-2-222-22-200-2200−i2−i2i2i2i2i2−i2−i20−2i2i2i−2i2i−2i−2i2i0−i2i2i2−i2-22002-200i2i2−i2−i2−i2−i2i2i2000000000000−222−22−2−22000000000000
χ6422-2-2-222-22-200-2200−i2−i2i2i2i2i2−i2−i20−2i2i2i−2i−2i2i2i−2i0−i2i2i2−i22-200-2200−i2−i2i2i2i2i2−i2−i2000000000000−222−2−222−2000000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000000040000000000000000000000000000000000000000000000000000
χ66444-4-4-4-44-4-4-4-4444400000000-40000000040000000000000000000000000000000000000000000000000000
χ6744-444-4-4-4-4400-44002i22i2−2i2−2i22i22i2−2i2−2i20000000000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ6844-444-4-4-4-4400-4400−2i2−2i22i22i2−2i2−2i22i22i200000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ6944-4-4-444-4-44004-4002i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ7044-4-4-444-4-44004-400−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ714-444-44-4-4000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000022−220022−222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ724-444-44-4-4000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000−222200−2222−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ734-444-44-4-400000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000022−220022−22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ744-444-44-4-400000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000−222200−22222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ754-44-44-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000022−2200−22222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ764-44-44-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000−22220022−22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ774-44-44-44-400000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000022−2200−2222−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ784-44-44-44-400000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000−22220022−222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ794-4-44-4-444004-4004-400000000000000000000000000000022−22−222222−22−222200000000000000000000000000000000
χ804-4-44-4-444004-4004-4000000000000000000000000000000−222222−22−222222−2200000000000000000000000000000000
χ814-4-44-4-44400-4400-444-4-444-4-4400000000000000000000000000000000000000000000000000000000000000
χ824-4-44-4-44400-4400-44-444-4-444-400000000000000000000000000000000000000000000000000000000000000
χ834-4-4-444-44004-400-4400000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000
χ844-4-4-444-44004-400-44000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000
χ854-4-4-444-4400-44004-44-4-44-444-400000000000000000000000000000000000000000000000000000000000000
χ864-4-4-444-4400-44004-4-444-44-4-4400000000000000000000000000000000000000000000000000000000000000

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