Finite Group Databasebeta

← Group #10829872

Character table — Group #10829872

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222224444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order12222234444444466612121212444444444466121212121212121212121212121212121212121212121212121244444444881212121224242424224444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1
χ91111111-1-1-1-111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111111-111-1-111-1-11-111-1-1-1-11-11-1
χ101111111-1-1-1-111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-11-111-1-111-1-1-11-1-11111-11-11
χ111111111-1-1-1-111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-111111-11-1-111-1-111-1111-1-1-1-1-11-11
χ121111111-1-1-1-111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11-1-111-1-1111-1-1-111111-11-1
χ131111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11111-1111-1-1-1-1111-1-1-1-1-1111-1-11
χ141111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-1-1111-1-1-1-111-111111-1-1-111-1
χ151111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111111-1-1-11111-1-1-11-1-1-1-111-111-1
χ161111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1-1-11-1-1-11111-1-11-11111-1-11-1-11
χ1722222222222-2-2-2-2222-2-2-2-2-2-20000000022-2-22222-2-2-2-20000000000000000000022-2-2000000000000002-2000000
χ1822222222222-2-2-2-2222-2-2-2-2-2-20000000022-2-22222-2-2-2-200000000000000000000-2-22200000000000000-22000000
χ192222222-2-2-2-2-2-2-2-2222-2-2-2-2220000000022-2-2-2-2-2-222220000000000000000000022-2-200000000000000-22000000
χ202222222-2-2-2-2-2-2-2-2222-2-2-2-2220000000022-2-2-2-2-2-2222200000000000000000000-2-222000000000000002-2000000
χ21222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1-1-1-1-1000000000000
χ22222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211111111000000000000
χ23222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122220000-2-2-1-1-1-11111000000000000
χ24222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-20000221111-1-1-1-1000000000000
χ25222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111112-22-200002-2-1-111-1-111000000000000
χ26222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111111111-22-220000-2211-1-111-1-1000000000000
χ27222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-12-22-20000-22-1-11111-1-1000000000000
χ28222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-22-2200002-211-1-1-1-111000000000000
χ292222-2-2222-2-22-22-222222222-200000000-2-2-2-222-2-222-2-2000000000000000000000000000000000022000000-2-200
χ302222-2-2222-2-22-22-222222222-200000000-2-2-2-222-2-222-2-20000000000000000000000000000000000-2-20000002200
χ312222-2-2222-2-2-22-22222-2-2-2-2-2200000000-2-22222-2-2-2-222000000000000000022-2-20000002-22-20000000000000000
χ322222-2-2222-2-2-22-22222-2-2-2-2-2200000000-2-22222-2-2-2-2220000000000000000-2-222000000-22-220000000000000000
χ332222-2-22-2-2222-22-22222222-2200000000-2-2-2-2-2-222-2-22200000000000000000000000000000000002-2000000-2200
χ342222-2-22-2-2222-22-22222222-2200000000-2-2-2-2-2-222-2-2220000000000000000000000000000000000-220000002-200
χ352222-2-22-2-222-22-22222-2-2-2-22-200000000-2-222-2-22222-2-200000000000000002-2-220000002-2-220000000000000000
χ362222-2-22-2-222-22-22222-2-2-2-22-200000000-2-222-2-22222-2-20000000000000000-222-2000000-222-20000000000000000
χ372222-2-2-122-2-2-22-22-1-1-11111-220000000011-1-1-1-11111-1-13333−3−3−3−33333−3−3−3−322-2-2000000-11-113−33−3000000000000
χ382222-2-2-122-2-2-22-22-1-1-11111-220000000011-1-1-1-11111-1-13333−3−3−3−33333−3−3−3−3-2-2220000001-11-1−33−33000000000000
χ392222-2-2-122-2-2-22-22-1-1-11111-220000000011-1-1-1-11111-1-1−3−3−3−33333−3−3−3−3333322-2-2000000-11-11−33−33000000000000
χ402222-2-2-122-2-2-22-22-1-1-11111-220000000011-1-1-1-11111-1-1−3−3−3−33333−3−3−3−33333-2-2220000001-11-13−33−3000000000000
χ412222-2-2-1-2-222-22-22-1-1-111112-20000000011-1-111-1-1-1-1113333−3−3−3−3−3−3−3−333332-2-22000000-111-13−3−33000000000000
χ422222-2-2-1-2-222-22-22-1-1-111112-20000000011-1-111-1-1-1-1113333−3−3−3−3−3−3−3−33333-222-20000001-1-11−333−3000000000000
χ432222-2-2-1-2-222-22-22-1-1-111112-20000000011-1-111-1-1-1-111−3−3−3−333333333−3−3−3−32-2-22000000-111-1−333−3000000000000
χ442222-2-2-1-2-222-22-22-1-1-111112-20000000011-1-111-1-1-1-111−3−3−3−333333333−3−3−3−3-222-20000001-1-113−3−33000000000000
χ452-2-222-2200002-2-222-2-222-2-20022-2-200002-22-20000000022-2-222-2-20000000000002i−2i2i−2i0000000000002i−2i00000000
χ462-2-222-2200002-2-222-2-222-2-20022-2-200002-22-20000000022-2-222-2-2000000000000−2i2i−2i2i000000000000−2i2i00000000
χ472-2-222-2200002-2-222-2-222-2-200-2-22200002-22-200000000-2-222-2-2220000000000002i−2i2i−2i000000000000−2i2i00000000
χ482-2-222-2200002-2-222-2-222-2-200-2-22200002-22-200000000-2-222-2-222000000000000−2i2i−2i2i0000000000002i−2i00000000
χ492-2-222-220000-222-22-2-2-2-2220000002i2i−2i−2i2-2-2200000000000000002i2i−2i−2i2i2i−2i−2i00002i−2i−2i2i00000000000000002-20000
χ502-2-222-220000-222-22-2-2-2-2220000002i2i−2i−2i2-2-2200000000000000002i2i−2i−2i2i2i−2i−2i0000−2i2i2i−2i0000000000000000-220000
χ512-2-222-220000-222-22-2-2-2-222000000−2i−2i2i2i2-2-220000000000000000−2i−2i2i2i−2i−2i2i2i00002i−2i−2i2i0000000000000000-220000
χ522-2-222-220000-222-22-2-2-2-222000000−2i−2i2i2i2-2-220000000000000000−2i−2i2i2i−2i−2i2i2i0000−2i2i2i−2i00000000000000002-20000
χ53444444-24444-4-4-4-4-2-2-22222-4-400000000-2-222-2-2-2-222220000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-4-4-2-2-222224400000000-2-2222222-2-2-2-20000000000000000000000000000000000000000000000
χ554444-4-4-244-4-44-44-4-2-2-2-2-2-2-24-4000000002222-2-222-2-2220000000000000000000000000000000000000000000000
χ564444-4-4-2-4-4444-44-4-2-2-2-2-2-2-2-4400000000222222-2-222-2-20000000000000000000000000000000000000000000000
χ5744-4-40044-4000000-44-40000002-22-22-22-200004-40000002-22-22-22-22-22-22-22-2000000000000000000000000000000
χ5844-4-40044-4000000-44-4000000-22-22-22-2200004-4000000-22-22-22-22-22-22-22-22000000000000000000000000000000
χ5944-4-4004-44000000-44-40000002-22-2-22-220000-440000002-22-22-22-2-22-22-22-22000000000000000000000000000000
χ6044-4-4004-44000000-44-4000000-22-222-22-20000-44000000-22-22-22-222-22-22-22-2000000000000000000000000000000
χ6144-4-400-24-40000002-2223−2323−23002-22-22-22-20000-220023−2300−1+31−3−1+31−3−1−31+3−1−31+3−1+31−3−1+31−3−1−31+3−1−31+3000000000000000000000000000000
χ6244-4-400-24-40000002-2223−2323−2300-22-22-22-220000-220023−23001−3−1+31−3−1+31+3−1−31+3−1−31−3−1+31−3−1+31+3−1−31+3−1−3000000000000000000000000000000
χ6344-4-400-24-40000002-22−2323−2323002-22-22-22-20000-2200−232300−1−31+3−1−31+3−1+31−3−1+31−3−1−31+3−1−31+3−1+31−3−1+31−3000000000000000000000000000000
χ6444-4-400-24-40000002-22−2323−232300-22-22-22-220000-2200−2323001+3−1−31+3−1−31−3−1+31−3−1+31+3−1−31+3−1−31−3−1+31−3−1+3000000000000000000000000000000
χ6544-4-400-2-440000002-2223−2323−23002-22-2-22-2200002-200−232300−1+31−3−1+31−3−1−31+3−1−31+31−3−1+31−3−1+31+3−1−31+3−1−3000000000000000000000000000000
χ6644-4-400-2-440000002-2223−2323−2300-22-222-22-200002-200−2323001−3−1+31−3−1+31+3−1−31+3−1−3−1+31−3−1+31−3−1−31+3−1−31+3000000000000000000000000000000
χ6744-4-400-2-440000002-22−2323−2323002-22-2-22-2200002-20023−2300−1−31+3−1−31+3−1+31−3−1+31−31+3−1−31+3−1−31−3−1+31−3−1+3000000000000000000000000000000
χ6844-4-400-2-440000002-22−2323−232300-22-222-22-200002-20023−23001+3−1−31+3−1−31−3−1+31−3−1+3−1−31+3−1−31+3−1+31−3−1+31−3000000000000000000000000000000
χ694-44-4004004i−4i0000-4-440000002-2-222i−2i−2i2i0000004i−4i00002-2-222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ704-44-4004004i−4i0000-4-44000000-222-2−2i2i2i−2i0000004i−4i0000-222-2-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ714-44-400400−4i4i0000-4-440000002-2-22−2i2i2i−2i000000−4i4i00002-2-222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ724-44-400400−4i4i0000-4-44000000-222-22i−2i−2i2i000000−4i4i0000-222-2-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ734-44-400-2004i−4i000022-223−23−2323002-2-222i−2i−2i2i000000−2i2i00−2i32i3−1+31−31−3−1+3−1−31+31+3−1−3−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+ζ11000000000000000000000000000000
χ744-44-400-2004i−4i000022-223−23−232300-222-2−2i2i2i−2i000000−2i2i00−2i32i31−3−1+3−1+31−31+3−1−3−1−31+3ζ2−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−ζ11000000000000000000000000000000
χ754-44-400-2004i−4i000022-2−232323−23002-2-222i−2i−2i2i000000−2i2i002i3−2i3−1−31+31+3−1−3−1+31−31−3−1+3ζ2+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+ζ11000000000000000000000000000000
χ764-44-400-2004i−4i000022-2−232323−2300-222-2−2i2i2i−2i000000−2i2i002i3−2i31+3−1−3−1−31+31−3−1+3−1+31−3−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−ζ11000000000000000000000000000000
χ774-44-400-200−4i4i000022-223−23−2323002-2-22−2i2i2i−2i0000002i−2i002i3−2i3−1+31−31−3−1+3−1−31+31+3−1−3ζ2−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−ζ11000000000000000000000000000000
χ784-44-400-200−4i4i000022-223−23−232300-222-22i−2i−2i2i0000002i−2i002i3−2i31−3−1+3−1+31−31+3−1−3−1−31+3−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+ζ11000000000000000000000000000000
χ794-44-400-200−4i4i000022-2−232323−23002-2-22−2i2i2i−2i0000002i−2i00−2i32i3−1−31+31+3−1−3−1+31−31−3−1+3−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−ζ11000000000000000000000000000000
χ804-44-400-200−4i4i000022-2−232323−2300-222-22i−2i−2i2i0000002i−2i00−2i32i31+3−1−3−1−31+31−3−1+3−1+31−3ζ2+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+ζ11000000000000000000000000000000
χ814-4-444-4-200004-4-44-222-2-2220044-4-40000-22-2200000000-2-222-2-22200000000000000000000000000000000000000
χ824-4-444-4-200004-4-44-222-2-22200-4-4440000-22-220000000022-2-222-2-200000000000000000000000000000000000000
χ834-4-444-4-20000-444-4-22222-2-20000004i4i−4i−4i-222-20000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000
χ844-4-444-4-20000-444-4-22222-2-2000000−4i−4i4i4i-222-200000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000
χ854-4-44-444000044-4-44-4-444-4-40000000000-44-44000000000000000000000000000000000000000000000000000000
χ864-4-44-4440000-4-4444-4-4-4-4440000000000-444-4000000000000000000000000000000000000000000000000000000
χ874-4-44-44-2000044-4-4-222-2-22200000000002-22-20000000000000000−2i3−2i32i32i32i32i3−2i3−2i3000000000000000000000000000000
χ884-4-44-44-2000044-4-4-222-2-22200000000002-22-200000000000000002i32i3−2i3−2i3−2i3−2i32i32i3000000000000000000000000000000
χ894-4-44-44-20000-4-444-22222-2-200000000002-2-22000000002323−23−23−23−23232300000000000000000000000000000000000000
χ904-4-44-44-20000-4-444-22222-2-200000000002-2-2200000000−23−2323232323−23−2300000000000000000000000000000000000000

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