Finite Group Databasebeta

← Group #211196

Character table — Group #211196

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444422224444444444888888884444888888888888888888888888888822224444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ5111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-111-1-1
χ9111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ10111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ11111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ12111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ13111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ14111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ15111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ16111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ17111-1-11-1-11iiii−i−i−i−i1-1-1-11-1111-1-11-1ii−i−i11-1-111-1-1ii−i−iii−i−i1-1i−iii−i−iii−i−i11-1-1ii−i−i11-1-111-1-11-11-1i−ii−i
χ18111-1-11-1-11iiii−i−i−i−i1-1-1-11-1111-1-11-1ii−i−i11-1-111-1-1ii−i−iii−i−i1-1i−i−i−iii−i−iii11-1-1ii−i−i-1-111-1-111-11-11−ii−ii
χ19111-1-11-1-11iiii−i−i−i−i1-1-1-11-1111-1-11-1ii−i−i11-1-1-1-111−i−iiiii−i−i-11−iiii−i−i−i−iii-1-111−i−iii11-1-1-1-1111-1-11i−i−ii
χ20111-1-11-1-11iiii−i−i−i−i1-1-1-11-1111-1-11-1ii−i−i11-1-1-1-111−i−iiiii−i−i-11−ii−i−iiiii−i−i-1-111−i−iii-1-11111-1-1-111-1−iii−i
χ21111-1-11-1-11iiii−i−i−i−i1-1-1-11-11-1-1111-1ii−i−i-1-11111-1-1ii−i−i−i−iii1-1i−iii−i−iii−i−i-1-111−i−iii11-1-111-1-1-11-11−ii−ii
χ22111-1-11-1-11iiii−i−i−i−i1-1-1-11-11-1-1111-1ii−i−i-1-11111-1-1ii−i−i−i−iii1-1i−i−i−iii−i−iii-1-111−i−iii-1-111-1-1111-11-1i−ii−i
χ23111-1-11-1-11iiii−i−i−i−i1-1-1-11-11-1-1111-1ii−i−i-1-111-1-111−i−iii−i−iii-11−iiii−i−i−i−iii11-1-1ii−i−i11-1-1-1-111-111-1−iii−i
χ24111-1-11-1-11iiii−i−i−i−i1-1-1-11-11-1-1111-1ii−i−i-1-111-1-111−i−iii−i−iii-11−ii−i−iiiii−i−i11-1-1ii−i−i-1-11111-1-11-1-11i−i−ii
χ25111-1-11-1-11−i−i−i−iiiii1-1-1-11-1111-1-11-1−i−iii11-1-111-1-1−i−iii−i−iii1-1−iiii−i−iii−i−i11-1-1−i−iii-1-111-1-111-11-11i−ii−i
χ26111-1-11-1-11−i−i−i−iiiii1-1-1-11-1111-1-11-1−i−iii11-1-111-1-1−i−iii−i−iii1-1−ii−i−iii−i−iii11-1-1−i−iii11-1-111-1-11-11-1−ii−ii
χ27111-1-11-1-11−i−i−i−iiiii1-1-1-11-1111-1-11-1−i−iii11-1-1-1-111ii−i−i−i−iii-11i−iii−i−i−i−iii-1-111ii−i−i-1-11111-1-1-111-1i−i−ii
χ28111-1-11-1-11−i−i−i−iiiii1-1-1-11-1111-1-11-1−i−iii11-1-1-1-111ii−i−i−i−iii-11i−i−i−iiiii−i−i-1-111ii−i−i11-1-1-1-1111-1-11−iii−i
χ29111-1-11-1-11−i−i−i−iiiii1-1-1-11-11-1-1111-1−i−iii-1-11111-1-1−i−iiiii−i−i1-1−iiii−i−iii−i−i-1-111ii−i−i-1-111-1-1111-11-1−ii−ii
χ30111-1-11-1-11−i−i−i−iiiii1-1-1-11-11-1-1111-1−i−iii-1-11111-1-1−i−iiiii−i−i1-1−ii−i−iii−i−iii-1-111ii−i−i11-1-111-1-1-11-11i−ii−i
χ31111-1-11-1-11−i−i−i−iiiii1-1-1-11-11-1-1111-1−i−iii-1-111-1-111ii−i−iii−i−i-11i−iii−i−i−i−iii11-1-1−i−iii-1-11111-1-11-1-11−iii−i
χ32111-1-11-1-11−i−i−i−iiiii1-1-1-11-11-1-1111-1−i−iii-1-111-1-111ii−i−iii−i−i-11i−i−i−iiiii−i−i11-1-1−i−iii11-1-1-1-111-111-1i−i−ii
χ3322222222222-2-222-2-2-2-222-2-222222-2-22-22-2-2-2-2-2000000002-22-2000000000000000000000000000000000000
χ3422222222222-2-222-2-2-2-222-2-22-2-2-2-2-2-22-22-2222200000000-22-22000000000000000000000000000000000000
χ35222222222-2-222-2-222-2-222-2-222222-2-2-22-22-2-2-2-200000000-22-22000000000000000000000000000000000000
χ36222222222-2-222-2-222-2-222-2-22-2-2-2-2-2-2-22-222222000000002-22-2000000000000000000000000000000000000
χ3722222222-22222222222-2-222-20000-2-2-2-2-2-20000222222220000-2-2-2-200000000000000000000000000000000
χ3822222222-22222222222-2-222-20000-2-2-2-2-2-20000-2-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ3922222222-222-2-222-2-2-2-2-2-2-2-2-2000022-22-2200000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ4022222222-222-2-222-2-2-2-2-2-2-2-2-2000022-22-220000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ4122222222-2-2-222-2-222-2-2-2-2-2-2-20000222-22-200000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ4222222222-2-2-222-2-222-2-2-2-2-2-2-20000222-22-20000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ4322222222-2-2-2-2-2-2-2-2-222-2-222-20000-2-2222200002222-2-2-2-20000-2-22200000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-222-2-222-20000-2-222220000-2-2-2-22222000022-2-200000000000000000000000000000000
χ45222-2-22-2-222i2i−2i−2i−2i−2i2i2i-22-2-2-22222-2-2-222i−2i−2i2i-2-222000000002i−2i−2i2i000000000000000000000000000000000000
χ46222-2-22-2-222i2i−2i−2i−2i−2i2i2i-22-2-2-222-2-222-222i−2i−2i2i22-2-200000000−2i2i2i−2i000000000000000000000000000000000000
χ47222-2-22-2-22−2i−2i2i2i2i2i−2i−2i-22-2-2-22222-2-2-22−2i2i2i−2i-2-22200000000−2i2i2i−2i000000000000000000000000000000000000
χ48222-2-22-2-22−2i−2i2i2i2i2i−2i−2i-22-2-2-222-2-222-22−2i2i2i−2i22-2-2000000002i−2i−2i2i000000000000000000000000000000000000
χ49222-2-22-2-2-22i2i2i2i−2i−2i−2i−2i2-2222-2-20000-22−2i−2i2i2i000022-2-22i2i−2i−2i0000-22−2i2i00000000000000000000000000000000
χ50222-2-22-2-2-22i2i2i2i−2i−2i−2i−2i2-2222-2-20000-22−2i−2i2i2i0000-2-222−2i−2i2i2i00002-22i−2i00000000000000000000000000000000
χ51222-2-22-2-2-22i2i−2i−2i−2i−2i2i2i-2222-22-200002-2−2i2i2i−2i00000000000000000000000000002i−2i−2i2i-222-20000000000000000
χ52222-2-22-2-2-22i2i−2i−2i−2i−2i2i2i-2222-22-200002-2−2i2i2i−2i0000000000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ53222-2-22-2-2-2−2i−2i2i2i2i2i−2i−2i-2222-22-200002-22i−2i−2i2i00000000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ54222-2-22-2-2-2−2i−2i2i2i2i2i−2i−2i-2222-22-200002-22i−2i−2i2i0000000000000000000000000000−2i2i2i−2i-222-20000000000000000
χ55222-2-22-2-2-2−2i−2i−2i−2i2i2i2i2i2-2222-2-20000-222i2i−2i−2i000022-2-2−2i−2i2i2i0000-222i−2i00000000000000000000000000000000
χ56222-2-22-2-2-2−2i−2i−2i−2i2i2i2i2i2-2222-2-20000-222i2i−2i−2i0000-2-2222i2i−2i−2i00002-2−2i2i00000000000000000000000000000000
χ572-2-2222-2-202i−2i2i−2i2i−2i2i−2i-22002-20000000000000002-22-22i−2i2i−2i00000000i2−i2i2−i2i2−i2i2−i2000000002−22−22−22−200000000
χ582-2-2222-2-202i−2i2i−2i2i−2i2i−2i-22002-20000000000000002-22-22i−2i2i−2i00000000−i2i2−i2i2−i2i2−i2i200000000−22−22−22−2200000000
χ592-2-2222-2-202i−2i2i−2i2i−2i2i−2i-22002-2000000000000000-22-22−2i2i−2i2i00000000i2−i2i2−i2−i2i2−i2i2000000002−22−2−22−2200000000
χ602-2-2222-2-202i−2i2i−2i2i−2i2i−2i-22002-2000000000000000-22-22−2i2i−2i2i00000000−i2i2−i2i2i2−i2i2−i200000000−22−222−22−200000000
χ612-2-2222-2-20−2i2i−2i2i−2i2i−2i2i-22002-20000000000000002-22-2−2i2i−2i2i00000000i2−i2i2−i2i2−i2i2−i200000000−22−22−22−2200000000
χ622-2-2222-2-20−2i2i−2i2i−2i2i−2i2i-22002-20000000000000002-22-2−2i2i−2i2i00000000−i2i2−i2i2−i2i2−i2i2000000002−22−22−22−200000000
χ632-2-2222-2-20−2i2i−2i2i−2i2i−2i2i-22002-2000000000000000-22-222i−2i2i−2i00000000i2−i2i2−i2−i2i2−i2i200000000−22−222−22−200000000
χ642-2-2222-2-20−2i2i−2i2i−2i2i−2i2i-22002-2000000000000000-22-222i−2i2i−2i00000000−i2i2−i2i2i2−i2i2−i2000000002−22−2−22−2200000000
χ652-2-2-2-222202-22-2-22-22-2-200220000000000000002-2-222-2-22000000002−2−222−2−22000000002−2−222−2−2200000000
χ662-2-2-2-222202-22-2-22-22-2-200220000000000000002-2-222-2-2200000000−222−2−222−200000000−222−2−222−200000000
χ672-2-2-2-222202-22-2-22-22-2-20022000000000000000-222-2-222-2000000002−2−22−222−2000000002−2−22−222−200000000
χ682-2-2-2-222202-22-2-22-22-2-20022000000000000000-222-2-222-200000000−222−22−2−2200000000−222−22−2−2200000000
χ692-2-2-2-22220-22-222-22-2-2-200220000000000000002-2-22-222-2000000002−2−222−2−2200000000−222−2−222−200000000
χ702-2-2-2-22220-22-222-22-2-2-200220000000000000002-2-22-222-200000000−222−2−222−2000000002−2−222−2−2200000000
χ712-2-2-2-22220-22-222-22-2-2-20022000000000000000-222-22-2-22000000002−2−22−222−200000000−222−22−2−2200000000
χ722-2-2-2-22220-22-222-22-2-2-20022000000000000000-222-22-2-2200000000−222−22−2−22000000002−2−22−222−200000000
χ7344-44-4-44-4400000000004-400-400000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ7444-44-4-44-4400000000004-400-40000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ7544-44-4-44-4-40000000000-440044-44-40000000000000000000000000000000000000000000000000000000000
χ7644-44-4-44-4-40000000000-44004-44-440000000000000000000000000000000000000000000000000000000000
χ7744-4-44-4-4440000000000-4400-400000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ7844-4-44-4-4440000000000-4400-40000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ7944-4-44-4-44-400000000004-40044-4-440000000000000000000000000000000000000000000000000000000000
χ8044-4-44-4-44-400000000004-4004-444-40000000000000000000000000000000000000000000000000000000000
χ814-4-4444-4-404i−4i−4i4i4i−4i−4i4i4-400-44000000000000000000000000000000000000000000000000000000000000000
χ824-4-4444-4-40−4i4i4i−4i−4i4i4i−4i4-400-44000000000000000000000000000000000000000000000000000000000000000
χ834-4-4-4-444404-4-44-444-44400-4-4000000000000000000000000000000000000000000000000000000000000000
χ844-4-4-4-44440-444-44-4-444400-4-4000000000000000000000000000000000000000000000000000000000000000
χ858-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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