Finite Group Databasebeta

← Group #10826853

Character table — Group #10826853

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222224444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order122222344444444666121212122244444444666666121212121212121212121212121212121212121212122444444468812121224242424222224444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111-1-1111-1-11-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111-1-1-1-1-1-111-1-1-111-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111111111-1-1
χ91111111-1-1-1-111111111111-1-11111-1-1-1-11-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1111-1-1-1-1111-1-1-1-111-1
χ101111111-1-1-1-111111111111-1-11111-1-1-1-11-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1111-1-111-1-1-11111-1-11
χ111111111-1-1-1-111111111111-1-11111-1-1-1-11-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-11111-1-1111-1-1-111-1-111-111-1-1-1-11
χ121111111-1-1-1-111111111111-1-11111-1-1-1-11-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1-11111-1-11-1-11111-1
χ131111111-1-1-1-111111111111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111111-11-1-11-1-111-1-1-1-11-1-1111-11
χ141111111-1-1-1-111111111111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-11-11-1-11-1-1111111-111-1-1-11-1
χ151111111-1-1-1-111111111111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-11111-11-111-111-1-1-1-1-1-1-11111-11-1
χ161111111-1-1-1-111111111111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-11-111-111-1-111111-1-1-1-11-11
χ1722222222222-2-2-2-2222-2-2-2-2-2-2000000002-2-2-2-22-2-222220000000000000000000022-2-200000000002-20000000000
χ1822222222222-2-2-2-2222-2-2-2-2-2-2000000002-2-2-2-22-2-2222200000000000000000000-2-2220000000000-220000000000
χ192222222-2-2-2-2-2-2-2-2222-2-2-2-22200000000222222-2-2-2-2-2-20000000000000000000022-2-20000000000-220000000000
χ202222222-2-2-2-2-2-2-2-2222-2-2-2-22200000000222222-2-2-2-2-2-200000000000000000000-2-22200000000002-20000000000
χ21222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000-122-1-1-1-1-1-1-1000000000000
χ22222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200001-2-21111111000000000000
χ23222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122220000-1-2-2-1-1-11111000000000000
χ24222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-20000122111-1-1-1-1000000000000
χ25222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-11111-1-1-11111-1-1-1-1-1-1-1-1111111112-2-220000-12-211-1-1-111000000000000
χ26222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-11111-1-1-11111-1-1-1-1-1-1-1-111111111-222-200001-22-1-1111-1-1000000000000
χ27222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-11111-1-1-1111111111111-1-1-1-1-1-1-1-12-2-220000-1-2211-111-1-1000000000000
χ28222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-11111-1-1-1111111111111-1-1-1-1-1-1-1-1-222-2000012-2-1-11-1-111000000000000
χ292222-2-2222-2-222-2-222222222-200000000-222-2-2-2-2-222-2-20000000000000000000000000000000000000022-200-200
χ302222-2-2222-2-222-2-222222222-200000000-222-2-2-2-2-222-2-200000000000000000000000000000000000000-2-2200200
χ312222-2-2222-2-2-2-222222-2-2-2-2-2200000000-2-2-222-22222-2-2000000000000000022-2-200002002-2-20000000000000000
χ322222-2-2222-2-2-2-222222-2-2-2-2-2200000000-2-2-222-22222-2-20000000000000000-2-2220000-200-2220000000000000000
χ332222-2-22-2-22222-2-22222222-2200000000-2-2-222-2-2-2-2-222000000000000000000000000000000000000002-2200-200
χ342222-2-22-2-22222-2-22222222-2200000000-2-2-222-2-2-2-2-22200000000000000000000000000000000000000-22-200200
χ352222-2-22-2-222-2-222222-2-2-2-22-200000000-222-2-2-222-2-22200000000000000002-22-20000200-22-20000000000000000
χ362222-2-22-2-222-2-222222-2-2-2-22-200000000-222-2-2-222-2-2220000000000000000-22-220000-2002-220000000000000000
χ372222-2-2-122-2-2-2-222-1-1-11111-2200000000111-1-11-1-1-1-1113333−3−3−3−33333−3−3−3−322-2-20000-100-1113−33−3000000000000
χ382222-2-2-122-2-2-2-222-1-1-11111-2200000000111-1-11-1-1-1-1113333−3−3−3−33333−3−3−3−3-2-22200001001-1-1−33−33000000000000
χ392222-2-2-122-2-2-2-222-1-1-11111-2200000000111-1-11-1-1-1-111−3−3−3−33333−3−3−3−3333322-2-20000-100-111−33−33000000000000
χ402222-2-2-122-2-2-2-222-1-1-11111-2200000000111-1-11-1-1-1-111−3−3−3−33333−3−3−3−33333-2-22200001001-1-13−33−3000000000000
χ412222-2-2-1-2-222-2-222-1-1-111112-2000000001-1-1111-1-111-1-13333−3−3−3−3−3−3−3−333332-22-20000-1001-113−3−33000000000000
χ422222-2-2-1-2-222-2-222-1-1-111112-2000000001-1-1111-1-111-1-13333−3−3−3−3−3−3−3−33333-22-220000100-11-1−333−3000000000000
χ432222-2-2-1-2-222-2-222-1-1-111112-2000000001-1-1111-1-111-1-1−3−3−3−333333333−3−3−3−32-22-20000-1001-11−333−3000000000000
χ442222-2-2-1-2-222-2-222-1-1-111112-2000000001-1-1111-1-111-1-1−3−3−3−333333333−3−3−3−3-22-220000100-11-13−3−33000000000000
χ452-2-22-22200002-22-2-2-2222-2-200000022-2-2-2000022-200000000000022-2-222-2-200002-22-2000000000000000002-2000
χ462-2-22-22200002-22-2-2-2222-2-200000022-2-2-2000022-200000000000022-2-222-2-20000-22-2200000000000000000-22000
χ472-2-22-22200002-22-2-2-2222-2-2000000-2-222-2000022-2000000000000-2-222-2-22200002-22-200000000000000000-22000
χ482-2-22-22200002-22-2-2-2222-2-2000000-2-222-2000022-2000000000000-2-222-2-2220000-22-22000000000000000002-2000
χ492-2-22-2220000-22-22-2-22-2-2220022-2-20000-200002-22000022-2-222-2-20000000000002-2-220000000000002-200000000
χ502-2-22-2220000-22-22-2-22-2-2220022-2-20000-200002-22000022-2-222-2-2000000000000-222-2000000000000-2200000000
χ512-2-22-2220000-22-22-2-22-2-22200-2-2220000-200002-220000-2-222-2-2220000000000002-2-22000000000000-2200000000
χ522-2-22-2220000-22-22-2-22-2-22200-2-2220000-200002-220000-2-222-2-222000000000000-222-20000000000002-200000000
χ53444444-24444-4-4-4-4-2-2-22222-4-400000000-22222-222-2-2-2-20000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-4-4-2-2-222224400000000-2-2-2-2-2-22222220000000000000000000000000000000000000000000000
χ554444-4-4-244-4-444-4-4-2-2-2-2-2-2-24-4000000002-2-222222-2-2220000000000000000000000000000000000000000000000
χ564444-4-4-2-4-44444-4-4-2-2-2-2-2-2-2-4400000000222-2-222222-2-20000000000000000000000000000000000000000000000
χ5744-4-4004004i−4i00004-4-40000002i−2i2i−2i2-22-200000000004i−4i2i−2i2i−2i2i−2i2i−2i2-22-22-22-2000000000000000000000000000000
χ5844-4-4004004i−4i00004-4-4000000−2i2i−2i2i-22-2200000000004i−4i−2i2i−2i2i−2i2i−2i2i-22-22-22-22000000000000000000000000000000
χ5944-4-400400−4i4i00004-4-40000002i−2i2i−2i-22-220000000000−4i4i2i−2i2i−2i2i−2i2i−2i-22-22-22-22000000000000000000000000000000
χ6044-4-400400−4i4i00004-4-4000000−2i2i−2i2i2-22-20000000000−4i4i−2i2i−2i2i−2i2i−2i2i2-22-22-22-2000000000000000000000000000000
χ6144-4-400-2004i−4i0000-22223−2323−23002i−2i2i−2i2-22-2000−2i32i300000−2i2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−1+31−3−1+31−3−1−31+3−1−31+3000000000000000000000000000000
χ6244-4-400-2004i−4i0000-22223−2323−2300−2i2i−2i2i-22-22000−2i32i300000−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ111−3−1+31−3−1+31+3−1−31+3−1−3000000000000000000000000000000
χ6344-4-400-2004i−4i0000-222−2323−2323002i−2i2i−2i2-22-20002i3−2i300000−2i2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−1−31+3−1−31+3−1+31−3−1+31−3000000000000000000000000000000
χ6444-4-400-2004i−4i0000-222−2323−232300−2i2i−2i2i-22-220002i3−2i300000−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ111+3−1−31+3−1−31−3−1+31−3−1+3000000000000000000000000000000
χ6544-4-400-200−4i4i0000-22223−2323−23002i−2i2i−2i-22-220002i3−2i3000002i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ111−3−1+31−3−1+31+3−1−31+3−1−3000000000000000000000000000000
χ6644-4-400-200−4i4i0000-22223−2323−2300−2i2i−2i2i2-22-20002i3−2i3000002i−2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−1+31−3−1+31−3−1−31+3−1−31+3000000000000000000000000000000
χ6744-4-400-200−4i4i0000-222−2323−2323002i−2i2i−2i-22-22000−2i32i3000002i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ111+3−1−31+3−1−31−3−1+31−3−1+3000000000000000000000000000000
χ6844-4-400-200−4i4i0000-222−2323−232300−2i2i−2i2i2-22-2000−2i32i3000002i−2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−1−31+3−1−31+3−1+31−3−1+31−3000000000000000000000000000000
χ694-44-40044i−4i000000-44-40000002i−2i−2i2i2-2-22000000004i−4i002i−2i−2i2i2i−2i−2i2i2-2-222-2-22000000000000000000000000000000
χ704-44-40044i−4i000000-44-4000000−2i2i2i−2i-222-2000000004i−4i00−2i2i2i−2i−2i2i2i−2i-222-2-222-2000000000000000000000000000000
χ714-44-4004−4i4i000000-44-40000002i−2i−2i2i-222-200000000−4i4i002i−2i−2i2i2i−2i−2i2i-222-2-222-2000000000000000000000000000000
χ724-44-4004−4i4i000000-44-4000000−2i2i2i−2i2-2-2200000000−4i4i00−2i2i2i−2i−2i2i2i−2i2-2-222-2-22000000000000000000000000000000
χ734-44-400-24i−4i0000002-2223−23−2323002i−2i−2i2i2-2-220−2i32i300000−2i2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−1+31−31−3−1+3−1−31+31+3−1−3000000000000000000000000000000
χ744-44-400-24i−4i0000002-2223−23−232300−2i2i2i−2i-222-20−2i32i300000−2i2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ111−3−1+3−1+31−31+3−1−3−1−31+3000000000000000000000000000000
χ754-44-400-24i−4i0000002-22−232323−23002i−2i−2i2i2-2-2202i3−2i300000−2i2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−1−31+31+3−1−3−1+31−31−3−1+3000000000000000000000000000000
χ764-44-400-24i−4i0000002-22−232323−2300−2i2i2i−2i-222-202i3−2i300000−2i2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ111+3−1−3−1−31+31−3−1+3−1+31−3000000000000000000000000000000
χ774-44-400-2−4i4i0000002-2223−23−2323002i−2i−2i2i-222-202i3−2i3000002i−2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ111−3−1+3−1+31−31+3−1−3−1−31+3000000000000000000000000000000
χ784-44-400-2−4i4i0000002-2223−23−232300−2i2i2i−2i2-2-2202i3−2i3000002i−2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−1+31−31−3−1+3−1−31+31+3−1−3000000000000000000000000000000
χ794-44-400-2−4i4i0000002-22−232323−23002i−2i−2i2i-222-20−2i32i3000002i−2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ111+3−1−3−1−31+31−3−1+3−1+31−3000000000000000000000000000000
χ804-44-400-2−4i4i0000002-22−232323−2300−2i2i2i−2i2-2-220−2i32i3000002i−2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−1−31+31+3−1−3−1+31−31−3−1+3000000000000000000000000000000
χ814-4-444-4400004-4-44-4-4444-4-4000000000040000-4-4400000000000000000000000000000000000000000000000000
χ824-4-444-440000-444-4-4-44-4-444000000000040000-44-400000000000000000000000000000000000000000000000000
χ834-4-444-4-200004-4-4422-2-2-2220000000000-2000022-200002323−23−23−23−23232300000000000000000000000000000000000000
χ844-4-444-4-200004-4-4422-2-2-2220000000000-2000022-20000−23−2323232323−23−2300000000000000000000000000000000000000
χ854-4-444-4-20000-444-422-222-2-20000000000-200002-220000000000002323−23−23−23−232323000000000000000000000000000000
χ864-4-444-4-20000-444-422-222-2-20000000000-200002-22000000000000−23−2323232323−23−23000000000000000000000000000000
χ874-4-44-44-200004-44-422-2-2-22200000044-4-420000-2-22000000000000-2-222-2-222000000000000000000000000000000
χ884-4-44-44-200004-44-422-2-2-222000000-4-44420000-2-2200000000000022-2-222-2-2000000000000000000000000000000
χ894-4-44-44-20000-44-4422-222-2-20044-4-4000020000-22-20000-2-222-2-22200000000000000000000000000000000000000
χ904-4-44-44-20000-44-4422-222-2-200-4-444000020000-22-2000022-2-222-2-200000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.