Finite Group Databasebeta

← Group #10712366

Character table — Group #10712366

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order1222223444466666668888888844448888121212121212121212121212242424242424242424242424242424242244666612121212224488881616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91-1-111-111-11-111-11-1-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1iiii−i−i−i−i1-11111-1-1-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-11-1ii−i−i11-1-1ii−i−i
χ101-1-111-111-11-111-11-1-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1iiii−i−i−i−i1-11111-1-1-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i-11-11−i−iii-1-111−i−iii
χ111-1-111-111-11-111-11-1-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1iiii−i−i−i−i1-11111-1-1-1-1iiii−i−i−i−i-11−ii-1-111−i−iii1-11-1ii−i−i-1-111−i−iii
χ121-1-111-111-11-111-11-1-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1iiii−i−i−i−i1-11111-1-1-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11-11−i−iii11-1-1ii−i−i
χ131-1-111-111-11-111-11-1-1-1−i−iii11-1-1−i−iii1-1−ii1-1−i−i−i−iiiii1-11111-1-1-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-11-1−i−iii11-1-1−i−iii
χ141-1-111-111-11-111-11-1-1-1−i−iii11-1-1−i−iii1-1−ii1-1−i−i−i−iiiii1-11111-1-1-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii-11-11ii−i−i-1-111ii−i−i
χ151-1-111-111-11-111-11-1-1-1−i−iii11-1-1−i−iii1-1−ii1-1−i−i−i−iiiii1-11111-1-1-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i1-11-1−i−iii-1-111ii−i−i
χ161-1-111-111-11-111-11-1-1-1−i−iii11-1-1−i−iii1-1−ii1-1−i−i−i−iiiii1-11111-1-1-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11-11ii−i−i11-1-1−i−iii
χ172222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ19222222-12222-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ20222222-12222-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ21222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-2-222-1-111111111-1-111111111-1-1-1-1-1-1-1-10000−i3i3−i3i3−i3i3−i3i30000000000000000
χ22222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-2-222-1-111111111-1-111111111-1-1-1-1-1-1-1-10000i3−i3i3−i3i3−i3i3−i30000000000000000
χ23222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-222-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ24222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-222-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ272222-2-222-2-22-2-222-2-2222220000000000-2-22-200000000-220000000022-2-222-2-2000000000000000000002−22−22−22−2
χ282222-2-222-2-22-2-222-2-2222220000000000-2-22-200000000-220000000022-2-222-2-200000000000000000000−22−22−22−22
χ292222-2-222-2-22-2-222-2-22-2-2-2-20000000000222-200000000-2200000000-2-222-2-222000000000000000000002−22−2−22−22
χ302222-2-222-2-22-2-222-2-22-2-2-2-20000000000222-200000000-2200000000-2-222-2-22200000000000000000000−22−222−22−2
χ312222-2-22-222-2-2-222-2-22000022220000-2-200-22000000002-222-2-222-2-20000000000000000000022-2-2000000000000
χ322222-2-22-222-2-2-222-2-22000022220000-2-200-22000000002-222-2-222-2-200000000000000000000-2-222000000000000
χ332222-2-22-222-2-2-222-2-220000-2-2-2-200002200-22000000002-2-2-222-2-2220000000000000000000000002i−2i2i−2i00000000
χ342222-2-22-222-2-2-222-2-220000-2-2-2-200002200-22000000002-2-2-222-2-222000000000000000000000000−2i2i−2i2i00000000
χ352-2-222-222-22-222-22-2-2-22i2i−2i−2i-2-222−2i−2i2i2i-222i−2i2-2−2i−2i−2i−2i2i2i2i2i2-2-2-2-2-222222i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ362-2-222-222-22-222-22-2-2-2−2i−2i2i2i-2-2222i2i−2i−2i-22−2i2i2-22i2i2i2i−2i−2i−2i−2i2-2-2-2-2-22222−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ372-2-222-2-12-22-2-1-11-11112i2i−2i−2i22-2-22i2i−2i−2i2-22i−2i-11−i−i−i−iiiii-11-1-1-1-11111−i−i−i−iiiii2-22i−2i-1-111−i−iii0000000000000000
χ382-2-222-2-12-22-2-1-11-11112i2i−2i−2i22-2-22i2i−2i−2i2-22i−2i-11−i−i−i−iiiii-11-1-1-1-11111−i−i−i−iiiii-22−2i2i11-1-1ii−i−i0000000000000000
χ392-2-222-2-12-22-2-1-11-11112i2i−2i−2i-2-222−2i−2i2i2i-222i−2i-11iiii−i−i−i−i-111111-1-1-1-1−i−i−i−iiiii0000−i3i3i3−i33−3−330000000000000000
χ402-2-222-2-12-22-2-1-11-11112i2i−2i−2i-2-222−2i−2i2i2i-222i−2i-11iiii−i−i−i−i-111111-1-1-1-1−i−i−i−iiiii0000i3−i3−i3i3−333−30000000000000000
χ412-2-222-2-12-22-2-1-11-1111−2i−2i2i2i22-2-2−2i−2i2i2i2-2−2i2i-11iiii−i−i−i−i-11-1-1-1-11111iiii−i−i−i−i2-2−2i2i-1-111ii−i−i0000000000000000
χ422-2-222-2-12-22-2-1-11-1111−2i−2i2i2i22-2-2−2i−2i2i2i2-2−2i2i-11iiii−i−i−i−i-11-1-1-1-11111iiii−i−i−i−i-222i−2i11-1-1−i−iii0000000000000000
χ432-2-222-2-12-22-2-1-11-1111−2i−2i2i2i-2-2222i2i−2i−2i-22−2i2i-11−i−i−i−iiiii-111111-1-1-1-1iiii−i−i−i−i0000−i3i3i3−i3−333−30000000000000000
χ442-2-222-2-12-22-2-1-11-1111−2i−2i2i2i-2-2222i2i−2i−2i-22−2i2i-11−i−i−i−iiiii-111111-1-1-1-1iiii−i−i−i−i0000i3−i3−i3i33−3−330000000000000000
χ452-2-22-22222-2-2-2-2-2222-22i2i−2i−2i0000000000−2i2i2200000000-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000002−2−22i2−i2−i2i2
χ462-2-22-22222-2-2-2-2-2222-22i2i−2i−2i0000000000−2i2i2200000000-2-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000−222−2−i2i2i2−i2
χ472-2-22-22222-2-2-2-2-2222-2−2i−2i2i2i00000000002i−2i2200000000-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000002−2−22−i2i2i2−i2
χ482-2-22-22222-2-2-2-2-2222-2−2i−2i2i2i00000000002i−2i2200000000-2-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000−222−2i2−i2−i2i2
χ492-2-22-222-2-222-2-2-2222-2000022-2-20000-2200-2-2000000002222-2-2-2-222000000000000000000002-2-22000000000000
χ502-2-22-222-2-222-2-2-2222-2000022-2-20000-2200-2-2000000002222-2-2-2-22200000000000000000000-222-2000000000000
χ512-2-22-222-2-222-2-2-2222-20000-2-22200002-200-2-20000000022-2-22222-2-20000000000000000000000002-2-2200000000
χ522-2-22-222-2-222-2-2-2222-20000-2-22200002-200-2-20000000022-2-22222-2-2000000000000000000000000-222-200000000
χ534444444-4-4-4-444444440000000000000000-4-400000000-4-400000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-2-2-2-2000000000000000022−2i3−2i32i32i3−2i3−2i32i32i32200000000000000000000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-2-2-2-2-20000000000000000222i32i3−2i3−2i32i32i3−2i3−2i32200000000000000000000000000000000000000000000
χ564444-4-4-24-4-4422-2-222-244440000000000-4-4-22000000002-200000000-2-222-2-2220000000000000000000000000000
χ574444-4-4-24-4-4422-2-222-2-4-4-4-4000000000044-22000000002-20000000022-2-222-2-20000000000000000000000000000
χ584444-4-4-2-444-422-2-222-2000044440000-4-4002-200000000-22-2-222-2-222000000000000000000000000000000000000
χ594444-4-4-2-444-422-2-222-20000-4-4-4-4000044002-200000000-2222-2-222-2-2000000000000000000000000000000000000
χ6044-4-40040000004-400-4−2i22i2−2i22i222−2222−222i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i0022−220022−2200−2i22i200−2i22i2000000000000000000000000000000
χ6144-4-40040000004-400-4−2i22i2−2i22i2−2222−2222−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i00−222200−222200−2i22i200−2i22i2000000000000000000000000000000
χ6244-4-40040000004-400-42i2−2i22i2−2i222−2222−22−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i0022−220022−22002i2−2i2002i2−2i2000000000000000000000000000000
χ6344-4-40040000004-400-42i2−2i22i2−2i2−2222−22222i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i00−222200−2222002i2−2i2002i2−2i2000000000000000000000000000000
χ6444-4-400-20000−2i32i3-22−2i32i32−2i22i2−2i22i222−2222−222i−2i2i−2i0000002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ2200−22i6−i6−22i6−i6i2−i26−6i2−i26−60000000000000000000000000000
χ6544-4-400-20000−2i32i3-22−2i32i32−2i22i2−2i22i2−2222−2222−2i2i−2i2i000000−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22002−2−i6i62−2−i6i6i2−i26−6i2−i26−60000000000000000000000000000
χ6644-4-400-20000−2i32i3-22−2i32i322i2−2i22i2−2i222−2222−22−2i2i−2i2i000000−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ2200−22i6−i6−22i6−i6−i2i2−66−i2i2−660000000000000000000000000000
χ6744-4-400-20000−2i32i3-22−2i32i322i2−2i22i2−2i2−2222−22222i−2i2i−2i0000002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ22002−2−i6i62−2−i6i6−i2i2−66−i2i2−660000000000000000000000000000
χ6844-4-400-200002i3−2i3-222i3−2i32−2i22i2−2i22i222−2222−222i−2i2i−2i0000002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ1400−22−i6i6−22−i6i6i2−i2−66i2−i2−660000000000000000000000000000
χ6944-4-400-200002i3−2i3-222i3−2i32−2i22i2−2i22i2−2222−2222−2i2i−2i2i000000−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14002−2i6−i62−2i6−i6i2−i2−66i2−i2−660000000000000000000000000000
χ7044-4-400-200002i3−2i3-222i3−2i322i2−2i22i2−2i222−2222−22−2i2i−2i2i000000−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ1400−22−i6i6−22−i6i6−i2i26−6−i2i26−60000000000000000000000000000
χ7144-4-400-200002i3−2i3-222i3−2i322i2−2i22i2−2i2−2222−22222i−2i2i−2i0000002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ14002−2i6−i62−2i6−i6−i2i26−6−i2i26−60000000000000000000000000000
χ724-44-4004000000-4-400422−22−222222−22−2222-222-2000000-22-222-22-20022−2200−22220022−2200−2222000000000000000000000000000000
χ734-44-4004000000-4-400422−22−2222−222222−222-2-220000002-22-2-22-2200−22220022−220022−2200−2222000000000000000000000000000000
χ744-44-4004000000-4-4004−222222−2222−22−22222-2-220000002-22-2-22-220022−2200−222200−22220022−22000000000000000000000000000000
χ754-44-4004000000-4-4004−222222−22−222222−22-222-2000000-22-222-22-200−22220022−2200−22220022−22000000000000000000000000000000
χ764-44-400-20000−2i32i3222i3−2i3-222−22−222222−22−2222-222-20000001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300−22i6−i62−2−i6i6−22i6−i62−2−i6i60000000000000000000000000000
χ774-44-400-20000−2i32i3222i3−2i3-222−22−2222−222222−222-2-22000000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3002−2−i6i6−22i6−i6−22i6−i62−2−i6i60000000000000000000000000000
χ784-44-400-20000−2i32i3222i3−2i3-2−222222−2222−22−22222-2-22000000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300−22i6−i62−2−i6i62−2−i6i6−22i6−i60000000000000000000000000000
χ794-44-400-20000−2i32i3222i3−2i3-2−222222−22−222222−22-222-20000001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3002−2−i6i6−22i6−i62−2−i6i6−22i6−i60000000000000000000000000000
χ804-44-400-200002i3−2i322−2i32i3-222−22−222222−22−2222-222-20000001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300−22−i6i62−2i6−i6−22−i6i62−2i6−i60000000000000000000000000000
χ814-44-400-200002i3−2i322−2i32i3-222−22−2222−222222−222-2-22000000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3002−2i6−i6−22−i6i6−22−i6i62−2i6−i60000000000000000000000000000
χ824-44-400-200002i3−2i322−2i32i3-2−222222−2222−22−22222-2-22000000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300−22−i6i62−2i6−i62−2i6−i6−22−i6i60000000000000000000000000000
χ834-44-400-200002i3−2i322−2i32i3-2−222222−22−222222−22-222-20000001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3002−2i6−i6−22−i6i62−2i6−i6−22−i6i60000000000000000000000000000
χ844-4-444-44-44-4444-44-4-4-40000000000000000-4400000000-4400000000000000000000000000000000000000000000
χ854-4-444-4-2-44-44-2-22-222200000000000000002-22323−23−23−23−2323232-200000000000000000000000000000000000000000000
χ864-4-444-4-2-44-44-2-22-222200000000000000002-2−23−2323232323−23−232-200000000000000000000000000000000000000000000
χ874-4-44-44-244-4-4222-2-2-224i4i−4i−4i0000000000−4i4i-2-2000000002200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ884-4-44-44-244-4-4222-2-2-22−4i−4i4i4i00000000004i−4i-2-20000000022000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ894-4-44-44-2-4-444222-2-2-22000044-4-40000-44002200000000-2-2-2-22222-2-2000000000000000000000000000000000000
χ904-4-44-44-2-4-444222-2-2-220000-4-44400004-4002200000000-2-222-2-2-2-222000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.