Finite Group Databasebeta

← Group #10693023

Character table — Group #10693023

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order12222234444446661212121244466888888881212121212124444121212121212121212122424242424242424222244448888888888242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111111-1-1-1-1-1-1111-1-1-1-111-111iiii−i−i−i−i-1-111-1-111-1-11-11111-1-1-1-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−ii−iii−i−i1-1i−i
χ101111111-1-1-1-1-1-1111-1-1-1-111-111iiii−i−i−i−i-1-111-1-111-1-11-11111-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−i−i−iiiiii−iii−i−i-11−ii
χ111111111-1-1-1-1-1-1111-1-1-1-111-111iiii−i−i−i−i-1-111-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i−ii−i−iii-11−ii
χ121111111-1-1-1-1-1-1111-1-1-1-111-111iiii−i−i−i−i-1-111-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii−ii−i−iii1-1i−i
χ131111111-1-1-1-1-1-1111-1-1-1-111-111−i−i−i−iiiii-1-111-1-111-1-11-11111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii−ii−i−iii1-1−ii
χ141111111-1-1-1-1-1-1111-1-1-1-111-111−i−i−i−iiiii-1-111-1-111-1-11-11111-1-1-1-1−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i−ii−i−iii-11i−i
χ151111111-1-1-1-1-1-1111-1-1-1-111-111−i−i−i−iiiii-1-111-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiiii−iii−i−i-11i−i
χ161111111-1-1-1-1-1-1111-1-1-1-111-111−i−i−i−iiiii-1-111-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii-1-111-1-111iiii−i−i−i−ii−iii−i−i1-1−ii
χ172222222222-2-222222222-2-2-2220000000022-2-2-2-20000-2-200000000000000002222-2-2-2-2000000000000000000
χ182222222222-2-222222222-2-2-2220000000022-2-2-2-20000-2-20000000000000000-2-2-2-22222000000000000000000
χ192222222-2-2-222-2222-2-2-2-2-2-222200000000-2-2-2-2220000-22000000000000000022-2-2-2-222000000000000000000
χ202222222-2-2-222-2222-2-2-2-2-2-222200000000-2-2-2-2220000-220000000000000000-2-22222-2-2000000000000000000
χ21222222-1222222-1-1-1-1-1-1-1222-1-122222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ22222222-1222222-1-1-1-1-1-1-1222-1-122222222-1-1-1-1-1-1-2-2-2-2-1-111111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-2-2-2-2-1-11111111111111111000000000000000022-1-1-1-10000
χ25222222-1-2-2-2-2-2-2-1-1-1111122-2-1-12i2i2i2i−2i−2i−2i−2i11-1-11122-2-2-11-1-1-1-11111−i−i−i−iiiii00000000000000002i−2i−i−iii0000
χ26222222-1-2-2-2-2-2-2-1-1-1111122-2-1-12i2i2i2i−2i−2i−2i−2i11-1-111-2-222-111111-1-1-1-1−i−i−i−iiiii0000000000000000−2i2iii−i−i0000
χ27222222-1-2-2-2-2-2-2-1-1-1111122-2-1-1−2i−2i−2i−2i2i2i2i2i11-1-11122-2-2-11-1-1-1-11111iiii−i−i−i−i0000000000000000−2i2iii−i−i0000
χ28222222-1-2-2-2-2-2-2-1-1-1111122-2-1-1−2i−2i−2i−2i2i2i2i2i11-1-111-2-222-111111-1-1-1-1iiii−i−i−i−i00000000000000002i−2i−i−iii0000
χ292222-2-222-2222-222222222-2-2-2-222-2-222-2-2-2-222220000-2-20000000022-2-222-2-200000000000000000000000000
χ302222-2-222-2222-222222222-2-2-2-2-2-222-2-222-2-222220000-2-200000000-2-222-2-22200000000000000000000000000
χ312222-2-222-22-2-2-22222222-222-2-200000000-2-2-2-2-2-20000220000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ322222-2-222-22-2-2-22222222-222-2-200000000-2-2-2-2-2-2000022000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ332222-2-22-22-2222222-2-2-2-2-22-2-2-20000000022-2-22200002-200000000000000000000000022-2-2-2-2220000000000
χ342222-2-22-22-2222222-2-2-2-2-22-2-2-20000000022-2-22200002-2000000000000000000000000-2-22222-2-20000000000
χ352222-2-22-22-2-2-22222-2-2-2-22-22-2-22i2i−2i−2i−2i−2i2i2i2222-2-20000-22000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ362222-2-22-22-2-2-22222-2-2-2-22-22-2-2−2i−2i2i2i2i2i−2i−2i2222-2-20000-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ372222-2-2-12-2222-2-1-1-1-1-1-1-12-2-21122-2-222-2-211-1-1-1-1000011−i3−i3i3i3−i3−i3i3i3-1-111-1-111000000000000000000−i3i3−i3i30000
χ382222-2-2-12-2222-2-1-1-1-1-1-1-12-2-21122-2-222-2-211-1-1-1-1000011i3i3−i3−i3i3i3−i3−i3-1-111-1-111000000000000000000i3−i3i3−i30000
χ392222-2-2-12-2222-2-1-1-1-1-1-1-12-2-211-2-222-2-22211-1-1-1-1000011−i3−i3i3i3−i3−i3i3i311-1-111-1-1000000000000000000i3−i3i3−i30000
χ402222-2-2-12-2222-2-1-1-1-1-1-1-12-2-211-2-222-2-22211-1-1-1-1000011i3i3−i3−i3i3i3−i3−i311-1-111-1-1000000000000000000−i3i3−i3i30000
χ412222-2-2-1-22-2-2-22-1-1-111112-22112i2i−2i−2i−2i−2i2i2i-1-1-1-11100001-1−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i0000000000000000003−3−330000
χ422222-2-2-1-22-2-2-22-1-1-111112-22112i2i−2i−2i−2i−2i2i2i-1-1-1-11100001-1i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i000000000000000000−333−30000
χ432222-2-2-1-22-2-2-22-1-1-111112-2211−2i−2i2i2i2i2i−2i−2i-1-1-1-11100001-1−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii000000000000000000−333−30000
χ442222-2-2-1-22-2-2-22-1-1-111112-2211−2i−2i2i2i2i2i−2i−2i-1-1-1-11100001-1i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii0000000000000000003−3−330000
χ4522-2-22-2222-200-22-2-222-2-20002-22−22−22−22−22-20000000000000000002−22−22−22−22-22-200002−22−22−22−20000000000
χ4622-2-22-2222-200-22-2-222-2-20002-22−22−22−22−22-20000000000000000002−22−22−22−2-22-220000−22−22−22−220000000000
χ4722-2-22-2222-200-22-2-222-2-20002-2−22−22−22−222-2000000000000000000−22−22−22−222-22-20000−22−22−22−220000000000
χ4822-2-22-2222-200-22-2-222-2-20002-2−22−22−22−222-2000000000000000000−22−22−22−22-22-2200002−22−22−22−20000000000
χ4922-2-22-22-2-220022-2-2-2-2220002-2−i2i2−i2i2i2−i2i2−i2-22000000000000000000−i2i2−i2i2i2−i2i2−i22-2-220000−i2i2−i2i2i2−i2i2−i20000000000
χ5022-2-22-22-2-220022-2-2-2-2220002-2−i2i2−i2i2i2−i2i2−i2-22000000000000000000−i2i2−i2i2i2−i2i2−i2-222-20000i2−i2i2−i2−i2i2−i2i20000000000
χ5122-2-22-22-2-220022-2-2-2-2220002-2i2−i2i2−i2−i2i2−i2i2-22000000000000000000i2−i2i2−i2−i2i2−i2i22-2-220000i2−i2i2−i2−i2i2−i2i20000000000
χ5222-2-22-22-2-220022-2-2-2-2220002-2i2−i2i2−i2−i2i2−i2i2-22000000000000000000i2−i2i2−i2−i2i2−i2i2-222-20000−i2i2−i2i2i2−i2i2−i20000000000
χ5322-2-2-2222-2-20022-2-222-2-2000-222−2−222−2−22-220000000000000000002−2−222−2−2200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i20000000000
χ5422-2-2-2222-2-20022-2-222-2-2000-222−2−222−2−22-220000000000000000002−2−222−2−220000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i20000000000
χ5522-2-2-2222-2-20022-2-222-2-2000-22−222−2−222−2-22000000000000000000−222−2−222−200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i20000000000
χ5622-2-2-2222-2-20022-2-222-2-2000-22−222−2−222−2-22000000000000000000−222−2−222−20000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i20000000000
χ5722-2-2-222-22200-22-2-2-2-222000-22−i2i2i2−i2i2−i2−i2i22-2000000000000000000−i2i2i2−i2i2−i2−i2i200002i−2i−2i2i−222−22−2−220000000000
χ5822-2-2-222-22200-22-2-2-2-222000-22−i2i2i2−i2i2−i2−i2i22-2000000000000000000−i2i2i2−i2i2−i2−i2i20000−2i2i2i−2i2−2−22−222−20000000000
χ5922-2-2-222-22200-22-2-2-2-222000-22i2−i2−i2i2−i2i2i2−i22-2000000000000000000i2−i2−i2i2−i2i2i2−i200002i−2i−2i2i2−2−22−222−20000000000
χ6022-2-2-222-22200-22-2-2-2-222000-22i2−i2−i2i2−i2i2i2−i22-2000000000000000000i2−i2−i2i2−i2i2i2−i20000−2i2i2i−2i−222−22−2−220000000000
χ61444444-2444-4-44-2-2-2-2-2-2-2-4-4-4-2-200000000-2-22222000022000000000000000000000000000000000000000000
χ62444444-2-4-4-444-4-2-2-22222-4-44-2-2000000002222-2-200002-2000000000000000000000000000000000000000000
χ634444-4-4-24-44-4-4-4-2-2-2-2-2-2-2-44422000000002222220000-2-2000000000000000000000000000000000000000000
χ644444-4-4-2-44-4444-2-2-22222-44-42200000000-2-222-2-20000-22000000000000000000000000000000000000000000
χ6544-4-44-4-244-400-4-222-2-222000-2222−2222−2222−2222−22-22000000000000000000−22−22−22−2200000000000000000000000000
χ6644-4-44-4-244-400-4-222-2-222000-22−2222−2222−2222−2222-220000000000000000002−22−22−22−200000000000000000000000000
χ6744-4-44-4-2-4-44004-22222-2-2000-22−2i22i2−2i22i22i2−2i22i2−2i22-2000000000000000000i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ6844-4-44-4-2-4-44004-22222-2-2000-222i2−2i22i2−2i2−2i22i2−2i22i22-2000000000000000000−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ6944-4-4-44-24-4-4004-222-2-2220002-222−22−222222−22−22222-2000000000000000000−222−2−222−200000000000000000000000000
χ7044-4-4-44-24-4-4004-222-2-2220002-2−222222−22−222222−222-20000000000000000002−2−222−2−2200000000000000000000000000
χ7144-4-4-44-2-44400-4-22222-2-20002-2−2i22i22i2−2i22i2−2i2−2i22i2-22000000000000000000i2−i2−i2i2−i2i2i2−i200000000000000000000000000
χ7244-4-4-44-2-44400-4-22222-2-20002-22i2−2i2−2i22i2−2i22i22i2−2i2-22000000000000000000−i2i2i2−i2i2−i2−i2i200000000000000000000000000
χ734-44-40040004i−4i0-44-40000000000000000000004i−4i2-22i−2i002-22-22i−2i2i−2i0000000000000000000000000000000000
χ744-44-40040004i−4i0-44-40000000000000000000004i−4i-22−2i2i00-22-22−2i2i−2i2i0000000000000000000000000000000000
χ754-44-4004000−4i4i0-44-4000000000000000000000−4i4i2-2−2i2i002-22-2−2i2i−2i2i0000000000000000000000000000000000
χ764-44-4004000−4i4i0-44-4000000000000000000000−4i4i-222i−2i00-22-222i−2i2i−2i0000000000000000000000000000000000
χ774-44-400-20004i−4i02-2223−2323−23000000000000000−2i32i3−2i2i2-22i−2i00−1−i31+i3−1+i31−i32ζ22−2ζ222ζ14−2ζ140000000000000000000000000000000000
χ784-44-400-20004i−4i02-2223−2323−23000000000000000−2i32i3−2i2i-22−2i2i001+i3−1−i31−i3−1+i3−2ζ222ζ22−2ζ142ζ140000000000000000000000000000000000
χ794-44-400-20004i−4i02-22−2323−23230000000000000002i3−2i3−2i2i2-22i−2i00−1+i31−i3−1−i31+i32ζ14−2ζ142ζ22−2ζ220000000000000000000000000000000000
χ804-44-400-20004i−4i02-22−2323−23230000000000000002i3−2i3−2i2i-22−2i2i001−i3−1+i31+i3−1−i3−2ζ142ζ14−2ζ222ζ220000000000000000000000000000000000
χ814-44-400-2000−4i4i02-2223−2323−230000000000000002i3−2i32i−2i2-2−2i2i00−1+i31−i3−1−i31+i3−2ζ142ζ14−2ζ222ζ220000000000000000000000000000000000
χ824-44-400-2000−4i4i02-2223−2323−230000000000000002i3−2i32i−2i-222i−2i001−i3−1+i31+i3−1−i32ζ14−2ζ142ζ22−2ζ220000000000000000000000000000000000
χ834-44-400-2000−4i4i02-22−2323−2323000000000000000−2i32i32i−2i2-2−2i2i00−1−i31+i3−1+i31−i3−2ζ222ζ22−2ζ142ζ140000000000000000000000000000000000
χ844-44-400-2000−4i4i02-22−2323−2323000000000000000−2i32i32i−2i-222i−2i001+i3−1−i31−i3−1+i32ζ22−2ζ222ζ14−2ζ140000000000000000000000000000000000
χ858-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000
χ878-8-8800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000

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