Finite Group Databasebeta

← Group #10686160

Character table — Group #10686160

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111111122222222222222224444444444444444446666666666668888888888888888888888888812121212121212121212161616162424242424242424
order122222223444444446666666448888888812121212121212124444444444444444888812122424242424242424242424242424242444888888881212121244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-11111-1-1-1-1
χ9111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-1iiii−i−i−i−i11-1-111-1-1ii−i−i
χ10111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111−i−iii11iiii−i−i−i−i−i−i−i−iiiii-1-1iiii−i−i−i−i-1-111-1-111−i−iii
χ11111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i11−i−i−i−iiiii11-1-1-1-111−i−iii
χ12111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111−i−iii11iiii−i−i−i−i−i−i−i−iiiii11−i−i−i−iiiii-1-11111-1-1ii−i−i
χ13111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-1−i−i−i−iiiii11-1-111-1-1−i−iii
χ14111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-1-1−i−i−i−iiiii-1-111-1-111ii−i−i
χ15111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii11iiii−i−i−i−i11-1-1-1-111ii−i−i
χ16111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i11iiii−i−i−i−i-1-11111-1-1−i−iii
χ17111-1-1-11-1111-1-111-1-1-1-1-1-11111-111-1-111-1-111-1-1-1-111ii−i−iii−i−iii−i−i1-11-11-11-11-111-1-111-1-111-1-111-1-1i−iii−i−iii−i−i1-11-1i−ii−ii−ii−i
χ18111-1-1-11-1111-1-111-1-1-1-1-1-11111-111-1-111-1-111-1-1-1-111ii−i−iii−i−iii−i−i-11-11-11-111-111-1-111-1-1-1-111-1-111i−iii−i−iii−i−i-11-11−ii−ii−ii−ii
χ19111-1-1-11-1111-1-111-1-1-1-1-1-11111-111-1-111-1-111-1-1-1-111−i−iii−i−iii−i−iii1-11-11-11-11-111-1-111-1-111-1-111-1-1−ii−i−iii−i−iii1-11-1−ii−ii−ii−ii
χ20111-1-1-11-1111-1-111-1-1-1-1-1-11111-111-1-111-1-111-1-1-1-111−i−iii−i−iii−i−iii-11-11-11-111-111-1-111-1-1-1-111-1-111−ii−i−iii−i−iii-11-11i−ii−ii−ii−i
χ21111-1-1-11-1111-1-111-1-1-1-1-1-11111-1-1-111-1-11111-1-1-1-111ii−i−iii−i−iii−i−i1-11-1-11-111-1-1-111-1-111-1-111-1-111i−i−i−iii−i−iii1-11-1i−ii−i−ii−ii
χ22111-1-1-11-1111-1-111-1-1-1-1-1-11111-1-1-111-1-11111-1-1-1-111ii−i−iii−i−iii−i−i-11-111-11-11-1-1-111-1-11111-1-111-1-1i−i−i−iii−i−iii-11-11−ii−iii−ii−i
χ23111-1-1-11-1111-1-111-1-1-1-1-1-11111-1-1-111-1-11111-1-1-1-111−i−iii−i−iii−i−iii1-11-1-11-111-1-1-111-1-111-1-111-1-111−iiii−i−iii−i−i1-11-1−ii−iii−ii−i
χ24111-1-1-11-1111-1-111-1-1-1-1-1-11111-1-1-111-1-11111-1-1-1-111−i−iii−i−iii−i−iii-11-111-11-11-1-1-111-1-11111-1-111-1-1−iiii−i−iii−i−i-11-11i−ii−i−ii−ii
χ25111-1-1-11-11-1-111-1-111-1-1-1-11111-1ii−i−i−i−iii-1-11111-1-1ii−i−i−i−iiiii−i−i1-1-11i−i−ii1-1ii−i−i−i−iiiii−i−i−i−iii−ii-1-11111-1-11-1-11i−i−ii-111-1
χ26111-1-1-11-11-1-111-1-111-1-1-1-11111-1ii−i−i−i−iii-1-11111-1-1ii−i−i−i−iiiii−i−i-111-1−iii−i1-1ii−i−i−i−iii−i−iiiii−i−i−ii-1-11111-1-1-111-1−iii−i1-1-11
χ27111-1-1-11-11-1-111-1-111-1-1-1-11111-1ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i−i−iii1-1-11i−i−ii1-1ii−i−i−i−iiiii−i−i−i−iiii−i11-1-1-1-1111-1-11−iii−i1-1-11
χ28111-1-1-11-11-1-111-1-111-1-1-1-11111-1ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i−i−iii-111-1−iii−i1-1ii−i−i−i−iii−i−iiiii−i−ii−i11-1-1-1-111-111-1i−i−ii-111-1
χ29111-1-1-11-11-1-111-1-111-1-1-1-11111-1−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iiiii−i−i1-1-11−iii−i1-1−i−iiiii−i−i−i−iiiii−i−i−ii11-1-1-1-1111-1-11i−i−ii1-1-11
χ30111-1-1-11-11-1-111-1-111-1-1-1-11111-1−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iiiii−i−i-111-1i−i−ii1-1−i−iiiii−i−iii−i−i−i−iii−ii11-1-1-1-111-111-1−iii−i-111-1
χ31111-1-1-11-11-1-111-1-111-1-1-1-11111-1−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i−i−iii1-1-11−iii−i1-1−i−iiiii−i−i−i−iiiii−i−ii−i-1-11111-1-11-1-11−iii−i-111-1
χ32111-1-1-11-11-1-111-1-111-1-1-1-11111-1−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i−i−iii-111-1i−i−ii1-1−i−iiiii−i−iii−i−i−i−iiii−i-1-11111-1-1-111-1i−i−ii1-1-11
χ332222222222-22-22-22-22222222-2-2000000002-222-2-22-22222-2-2-2-2-2-2-2-200000000-2-200000000000000002200000000000000000000
χ342222222222-22-22-22-22222222-2-2000000002-222-2-22-2-2-2-2-22222222200000000-2-20000000000000000-2-200000000000000000000
χ35222222222-22-22-22-222222222-2-200000000-22-2-222-2222222222-2-2-2-200000000-2-20000000000000000-2-200000000000000000000
χ36222222222-22-22-22-222222222-2-200000000-22-2-222-22-2-2-2-2-2-2-2-2222200000000-2-200000000000000002200000000000000000000
χ3722222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000-1-1-1-100000000
χ3822222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000111100000000
χ3922222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000000000002222-2-2-2-2-1-111111111111111110000000000-1-1-1-100000000
χ4022222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000000000-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-10000000000111100000000
χ4122222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i2i2i−2i−2i−2i−2i1111111100000000000022-2-22i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii0000000000-1-11100000000
χ4222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i2i2i−2i−2i−2i−2i11111111000000000000-2-222−2i−2i2i2i-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000011-1-100000000
χ4322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i−2i−2i2i2i2i2i1111111100000000000022-2-2−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i0000000000-1-11100000000
χ4422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i−2i−2i2i2i2i2i11111111000000000000-2-2222i2i−2i−2i-1-1iiii−i−i−i−i−i−i−i−iiiii000000000011-1-100000000
χ45222-2-2-22-222-2-222-2-22-2-2-2-2222-22000000002-2-2-2222-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000-2200000000000000002i−2i00000000000000000000
χ46222-2-2-22-222-2-222-2-22-2-2-2-2222-22000000002-2-2-2222-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000-220000000000000000−2i2i00000000000000000000
χ47222-2-2-22-22-222-2-222-2-2-2-2-2222-2200000000-2222-2-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000-220000000000000000−2i2i00000000000000000000
χ48222-2-2-22-22-222-2-222-2-2-2-2-2222-2200000000-2222-2-2-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000-2200000000000000002i−2i00000000000000000000
χ49222-2-2-22-2-122-2-222-2-21111-1-1-12-222-2-222-2-2-1-11111-1-10000000000002-22-22-22-2-11-1-111-1-111-1-111-1-1110000000000-11-1100000000
χ50222-2-2-22-2-122-2-222-2-21111-1-1-12-222-2-222-2-2-1-11111-1-1000000000000-22-22-22-22-11-1-111-1-11111-1-111-1-100000000001-11-100000000
χ51222-2-2-22-2-122-2-222-2-21111-1-1-12-2-2-222-2-222-1-11111-1-10000000000002-22-2-22-22-1111-1-111-1-111-1-111-1-10000000000-11-1100000000
χ52222-2-2-22-2-122-2-222-2-21111-1-1-12-2-2-222-2-222-1-11111-1-1000000000000-22-222-22-2-1111-1-111-1-1-1-111-1-11100000000001-11-100000000
χ53222-2-2-22-2-1-2-222-2-2221111-1-1-12-22i2i−2i−2i−2i−2i2i2i11-1-1-1-1110000000000002-2-222i−2i−2i2i-11−i−iiiii−i−i−i−iiiii−i−i0000000000-111-100000000
χ54222-2-2-22-2-1-2-222-2-2221111-1-1-12-22i2i−2i−2i−2i−2i2i2i11-1-1-1-111000000000000-222-2−2i2i2i−2i-11−i−iiiii−i−iii−i−i−i−iii00000000001-1-1100000000
χ55222-2-2-22-2-1-2-222-2-2221111-1-1-12-2−2i−2i2i2i2i2i−2i−2i11-1-1-1-1110000000000002-2-22−2i2i2i−2i-11ii−i−i−i−iiiii−i−i−i−iii0000000000-111-100000000
χ56222-2-2-22-2-1-2-222-2-2221111-1-1-12-2−2i−2i2i2i2i2i−2i−2i11-1-1-1-111000000000000-222-22i−2i−2i2i-11ii−i−i−i−iii−i−iiiii−i−i00000000001-1-1100000000
χ5722-222-2-2-2202020-20-222-2-22-2-2002−22−22−22−202002-20-22-22-22-22-2000000000000002−22−22−22−200000000002−22−22−22−2000000000000
χ5822-222-2-2-2202020-20-222-2-22-2-2002−22−22−22−202002-20-2-22-22-22-22000000000000002−22−22−22−20000000000−22−22−22−22000000000000
χ5922-222-2-2-2202020-20-222-2-22-2-200−22−22−22−2202002-20-22-22-22-22-200000000000000−22−22−22−220000000000−22−22−22−22000000000000
χ6022-222-2-2-2202020-20-222-2-22-2-200−22−22−22−2202002-20-2-22-22-22-2200000000000000−22−22−22−2200000000002−22−22−22−2000000000000
χ6122-222-2-2-220-20-2020222-2-22-2-200−i2i2−i2i2i2−i2i2−i20-200-22022-22-2-22-2200000000000000−i2i2−i2i2i2−i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ6222-222-2-2-220-20-2020222-2-22-2-200−i2i2−i2i2i2−i2i2−i20-200-2202-22-222-22-200000000000000−i2i2−i2i2i2−i2i2−i20000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ6322-222-2-2-220-20-2020222-2-22-2-200i2−i2i2−i2−i2i2−i2i20-200-22022-22-2-22-2200000000000000i2−i2i2−i2−i2i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ6422-222-2-2-220-20-2020222-2-22-2-200i2−i2i2−i2−i2i2−i2i20-200-2202-22-222-22-200000000000000i2−i2i2−i2−i2i2−i2i20000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ6522-2-2-22-222020-20-202-2-2222-2-2002−2−222−2−220200-220-22i−2i−2i2i2i−2i−2i2i000000000000002−2−222−2−220000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ6622-2-2-22-222020-20-202-2-2222-2-2002−2−222−2−220200-220-2−2i2i2i−2i−2i2i2i−2i000000000000002−2−222−2−220000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ6722-2-2-22-222020-20-202-2-2222-2-200−222−2−222−20200-220-22i−2i−2i2i2i−2i−2i2i00000000000000−222−2−222−20000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ6822-2-2-22-222020-20-202-2-2222-2-200−222−2−222−20200-220-2−2i2i2i−2i−2i2i2i−2i00000000000000−222−2−222−20000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ6922-2-2-22-2220-202020-2-2-2222-2-200−i2i2i2−i2i2−i2−i2i20-2002-2022i−2i−2i2i−2i2i2i−2i00000000000000−i2i2i2−i2i2−i2−i2i200000000002−2−22−222−2000000000000
χ7022-2-2-22-2220-202020-2-2-2222-2-200−i2i2i2−i2i2−i2−i2i20-2002-202−2i2i2i−2i2i−2i−2i2i00000000000000−i2i2i2−i2i2−i2−i2i20000000000−222−22−2−22000000000000
χ7122-2-2-22-2220-202020-2-2-2222-2-200i2−i2−i2i2−i2i2i2−i20-2002-2022i−2i−2i2i−2i2i2i−2i00000000000000i2−i2−i2i2−i2i2i2−i20000000000−222−22−2−22000000000000
χ7222-2-2-22-2220-202020-2-2-2222-2-200i2−i2−i2i2−i2i2i2−i20-2002-202−2i2i2i−2i2i−2i−2i2i00000000000000i2−i2−i2i2−i2i2i2−i200000000002−2−22−222−2000000000000
χ7344444444-24-44-44-44-4-2-2-2-2-2-2-2-4-400000000-22-2-222-22000000000000000000002200000000000000000000000000000000000000
χ7444444444-2-44-44-44-44-2-2-2-2-2-2-2-4-4000000002-222-2-22-2000000000000000000002200000000000000000000000000000000000000
χ75444-4-4-44-4-24-4-444-4-442222-2-2-2-4400000000-2222-2-2-22000000000000000000002-200000000000000000000000000000000000000
χ76444-4-4-44-4-2-444-4-444-42222-2-2-2-44000000002-2-2-2222-2000000000000000000002-200000000000000000000000000000000000000
χ7744-444-4-4-4-204040-40-4-2-222-2220022−2222−2222−2222−220-200-22020000000000000000000000−22−22−22−22000000000000000000000000000000
χ7844-444-4-4-4-204040-40-4-2-222-22200−2222−2222−2222−22220-200-220200000000000000000000002−22−22−22−2000000000000000000000000000000
χ7944-444-4-4-4-20-40-40404-2-222-22200−2i22i2−2i22i22i2−2i22i2−2i202002-20-20000000000000000000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000000000
χ8044-444-4-4-4-20-40-40404-2-222-222002i2−2i22i2−2i2−2i22i2−2i22i202002-20-20000000000000000000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000000000
χ8144-4-4-44-44-2040-40-40422-2-2-2220022−22−222222−22−22220-2002-2020000000000000000000000−222−2−222−2000000000000000000000000000000
χ8244-4-4-44-44-2040-40-40422-2-2-22200−222222−22−222222−220-2002-20200000000000000000000002−2−222−2−22000000000000000000000000000000
χ8344-4-4-44-44-20-404040-422-2-2-22200−2i22i22i2−2i22i2−2i2−2i22i20200-220-20000000000000000000000i2−i2−i2i2−i2i2i2−i2000000000000000000000000000000
χ8444-4-4-44-44-20-404040-422-2-2-222002i2−2i2−2i22i2−2i22i22i2−2i20200-220-20000000000000000000000−i2i2i2−i2i2−i2−i2i2000000000000000000000000000000
χ854-444-44-4-4440-40-40404-44-4-44-40000000000404-400-40000000000000000000000000000000000000000000000000000000000000
χ864-444-44-4-44-404040-404-44-4-44-40000000000-40-440040000000000000000000000000000000000000000000000000000000000000
χ874-444-44-4-4-240-40-4040-22-222-220000000000-20-220020000000000000000000000000000000i6−i6i6−i6i6−i6i6−i60000000000000000000000
χ884-444-44-4-4-240-40-4040-22-222-220000000000-20-220020000000000000000000000000000000−i6i6−i6i6−i6i6−i6i60000000000000000000000
χ894-444-44-4-4-2-404040-40-22-222-220000000000202-200-200000000000000000000000000000006−66−6−66−660000000000000000000000
χ904-444-44-4-4-2-404040-40-22-222-220000000000202-200-20000000000000000000000000000000−66−666−66−60000000000000000000000
χ914-44-44-4-4444040-40-40-44-44-44-4000000000040-4400-40000000000000000000000000000000000000000000000000000000000000
χ924-44-44-4-444-40-404040-44-44-44-40000000000-404-40040000000000000000000000000000000000000000000000000000000000000
χ934-44-44-4-44-24040-40-402-22-22-220000000000-202-20020000000000000000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ944-44-44-4-44-24040-40-402-22-22-220000000000-202-20020000000000000000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ954-44-44-4-44-2-40-4040402-22-22-22000000000020-2200-200000000000000000000000000000006−6−66−666−60000000000000000000000
χ964-44-44-4-44-2-40-4040402-22-22-22000000000020-2200-20000000000000000000000000000000−666−66−6−660000000000000000000000
χ974-4-44-4-4444000000004-4-44-4-44000000000000000000000000004-44-4000000000000000000000000000000000000000000000000
χ984-4-44-4-4444000000004-4-44-4-4400000000000000000000000000-44-44000000000000000000000000000000000000000000000000
χ994-4-4-4444-4400000000-444-4-4-44000000000000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ1004-4-4-4444-4400000000-444-4-4-4400000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ1018-8-88-8-888-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8-8888-8-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000000000000000000000

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