Finite Group Databasebeta

← Group #10848632

Character table — Group #10848632

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222224444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order12222234444444466612121212444444444466121212121212121212121212121212121212121212121212121244444444881212121224242424222444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-11-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1111111-1-1
χ91111111-1-1-1-111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111111-111-1-111-1-1-111-1-1-111-1-11-1
χ101111111-1-1-1-111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-1-111-1-11-1-1111-1-111-11
χ111111111-1-1-1-111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-11-1-111-1-111-1-1-1-11111-1-1-11
χ121111111-1-1-1-111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-1-1111111-1-1-1-1111-1
χ131111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1111-1-1-1-111-111-1-1-1-1-111-11
χ141111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1111-1-1-1-1111-1-111111-1-11-1
χ151111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111111-1-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-1-11111-1-11111-1-111-1-1-11
χ17222222222-2-2-2-2-2-2222-2-2-2-22-20000000022-2-22222-2-2-2-2000000000000000000000000000000000002-202-2000000
χ18222222222-2-2-2-2-2-2222-2-2-2-22-20000000022-2-22222-2-2-2-200000000000000000000000000000000000-220-22000000
χ192222222-2-222-2-2-2-2222-2-2-2-2-220000000022-2-2-2-2-2-22222000000000000000000000000000000000002-20-22000000
χ202222222-2-222-2-2-2-2222-2-2-2-2-220000000022-2-2-2-2-2-2222200000000000000000000000000000000000-2202-2000000
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
χ25222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-11111111122-2-200002-2-1-111-1-111000000000000
χ26222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111111111-2-2220000-2211-1-111-1-1000000000000
χ27222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-122-2-20000-22-1-11111-1-1000000000000
χ28222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-2-22200002-211-1-1-1-111000000000000
χ292222-2-222222-2-222222-2-2-2-2-2-200000000-2-22222-2-222-2-200000000000000002-22-20000002-22-20000000000000000
χ302222-2-222222-2-222222-2-2-2-2-2-200000000-2-22222-2-222-2-20000000000000000-22-22000000-22-220000000000000000
χ312222-2-2222-2-222-2-22222222-2200000000-2-2-2-222-2-2-2-2220000000000000000000022-2-20000000000200-200000000
χ322222-2-2222-2-222-2-22222222-2200000000-2-2-2-222-2-2-2-22200000000000000000000-2-2220000000000-200200000000
χ332222-2-22-2-22222-2-222222222-200000000-2-2-2-2-2-22222-2-20000000000000000000022-2-20000000000-200200000000
χ342222-2-22-2-22222-2-222222222-200000000-2-2-2-2-2-22222-2-200000000000000000000-2-2220000000000200-200000000
χ352222-2-22-2-2-2-2-2-222222-2-2-2-22200000000-2-222-2-222-2-22200000000000000002-2-220000002-2-220000000000000000
χ362222-2-22-2-2-2-2-2-222222-2-2-2-22200000000-2-222-2-222-2-2220000000000000000-222-2000000-222-20000000000000000
χ372222-2-2-12222-2-222-1-1-11111-2-20000000011-1-1-1-111-1-1113333−3−3−3−33333−3−3−3−32-22-2000000-11-113−33−3000000000000
χ382222-2-2-12222-2-222-1-1-11111-2-20000000011-1-1-1-111-1-1113333−3−3−3−33333−3−3−3−3-22-220000001-11-1−33−33000000000000
χ392222-2-2-12222-2-222-1-1-11111-2-20000000011-1-1-1-111-1-111−3−3−3−33333−3−3−3−333332-22-2000000-11-11−33−33000000000000
χ402222-2-2-12222-2-222-1-1-11111-2-20000000011-1-1-1-111-1-111−3−3−3−33333−3−3−3−33333-22-220000001-11-13−33−3000000000000
χ412222-2-2-1-2-2-2-2-2-222-1-1-11111220000000011-1-111-1-111-1-13333−3−3−3−3−3−3−3−333332-2-22000000-111-13−3−33000000000000
χ422222-2-2-1-2-2-2-2-2-222-1-1-11111220000000011-1-111-1-111-1-13333−3−3−3−3−3−3−3−33333-222-20000001-1-11−333−3000000000000
χ432222-2-2-1-2-2-2-2-2-222-1-1-11111220000000011-1-111-1-111-1-1−3−3−3−333333333−3−3−3−32-2-22000000-111-1−333−3000000000000
χ442222-2-2-1-2-2-2-2-2-222-1-1-11111220000000011-1-111-1-111-1-1−3−3−3−333333333−3−3−3−3-222-20000001-1-113−3−33000000000000
χ452-2-222-2200002-22-22-2-222-2-200000022-2-22-22-2000000000000000022-2-222-2-200002i−2i2i−2i0000000000000000002i−2i00
χ462-2-222-2200002-22-22-2-222-2-200000022-2-22-22-2000000000000000022-2-222-2-20000−2i2i−2i2i000000000000000000−2i2i00
χ472-2-222-2200002-22-22-2-222-2-2000000-2-2222-22-20000000000000000-2-222-2-22200002i−2i2i−2i000000000000000000−2i2i00
χ482-2-222-2200002-22-22-2-222-2-2000000-2-2222-22-20000000000000000-2-222-2-2220000−2i2i−2i2i0000000000000000002i−2i00
χ492-2-22-22200002-2-222-2-222-2-20022-2-20000-22-220000000022-2-222-2-20000000000002i−2i−2i2i00000000000000002i−2i0000
χ502-2-22-22200002-2-222-2-222-2-20022-2-20000-22-220000000022-2-222-2-2000000000000−2i2i2i−2i0000000000000000−2i2i0000
χ512-2-22-22200002-2-222-2-222-2-200-2-2220000-22-2200000000-2-222-2-2220000000000002i−2i−2i2i0000000000000000−2i2i0000
χ522-2-22-22200002-2-222-2-222-2-200-2-2220000-22-2200000000-2-222-2-222000000000000−2i2i2i−2i00000000000000002i−2i0000
χ53444444-244-4-4-4-4-4-4-2-2-222224-400000000-2-222-2-2-2-222220000000000000000000000000000000000000000000000
χ54444444-2-4-444-4-4-4-4-2-2-22222-4400000000-2-2222222-2-2-2-20000000000000000000000000000000000000000000000
χ554444-4-4-244-4-444-4-4-2-2-2-2-2-2-2-44000000002222-2-22222-2-20000000000000000000000000000000000000000000000
χ564444-4-4-2-4-44444-4-4-2-2-2-2-2-2-24-400000000222222-2-2-2-2220000000000000000000000000000000000000000000000
χ5744-4-4004004i−4i0000-44-40000002-22-22i−2i2i−2i000000004i−4i002-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ5844-4-4004004i−4i0000-44-4000000-22-22−2i2i−2i2i000000004i−4i00-22-22-22-22−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ5944-4-400400−4i4i0000-44-40000002-22-2−2i2i−2i2i00000000−4i4i002-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ6044-4-400400−4i4i0000-44-4000000-22-222i−2i2i−2i00000000−4i4i00-22-22-22-222i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ6144-4-400-2004i−4i00002-2223−2323−23002-22-22i−2i2i−2i000000−2i32i3−2i2i00−1+31−3−1+31−3−1−31+3−1−31+3ζ2+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−ζ11000000000000000000000000000000
χ6244-4-400-2004i−4i00002-2223−2323−2300-22-22−2i2i−2i2i000000−2i32i3−2i2i001−3−1+31−3−1+31+3−1−31+3−1−3−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+ζ11000000000000000000000000000000
χ6344-4-400-2004i−4i00002-22−2323−2323002-22-22i−2i2i−2i0000002i3−2i3−2i2i00−1−31+3−1−31+3−1+31−3−1+31−3−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−ζ11000000000000000000000000000000
χ6444-4-400-2004i−4i00002-22−2323−232300-22-22−2i2i−2i2i0000002i3−2i3−2i2i001+3−1−31+3−1−31−3−1+31−3−1+3ζ2−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+ζ11000000000000000000000000000000
χ6544-4-400-200−4i4i00002-2223−2323−23002-22-2−2i2i−2i2i0000002i3−2i32i−2i00−1+31−3−1+31−3−1−31+3−1−31+3−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+ζ11000000000000000000000000000000
χ6644-4-400-200−4i4i00002-2223−2323−2300-22-222i−2i2i−2i0000002i3−2i32i−2i001−3−1+31−3−1+31+3−1−31+3−1−3ζ2+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−ζ11000000000000000000000000000000
χ6744-4-400-200−4i4i00002-22−2323−2323002-22-2−2i2i−2i2i000000−2i32i32i−2i00−1−31+3−1−31+3−1+31−3−1+31−3ζ2−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+ζ11000000000000000000000000000000
χ6844-4-400-200−4i4i00002-22−2323−232300-22-222i−2i2i−2i000000−2i32i32i−2i001+3−1−31+3−1−31−3−1+31−3−1+3−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−ζ11000000000000000000000000000000
χ694-44-40044i−4i000000-4-440000002-2-222i−2i−2i2i00004i−4i0000002-2-222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ704-44-40044i−4i000000-4-44000000-222-2−2i2i2i−2i00004i−4i000000-222-2-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ714-44-4004−4i4i000000-4-440000002-2-22−2i2i2i−2i0000−4i4i0000002-2-222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ724-44-4004−4i4i000000-4-44000000-222-22i−2i−2i2i0000−4i4i000000-222-2-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ734-44-400-24i−4i00000022-223−23−2323002-2-222i−2i−2i2i0000−2i2i0000−2i32i3−1+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
χ744-44-400-24i−4i00000022-223−23−232300-222-2−2i2i2i−2i0000−2i2i0000−2i32i31−3−1+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
χ754-44-400-24i−4i00000022-2−232323−23002-2-222i−2i−2i2i0000−2i2i00002i3−2i3−1−31+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
χ764-44-400-24i−4i00000022-2−232323−2300-222-2−2i2i2i−2i0000−2i2i00002i3−2i31+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
χ774-44-400-2−4i4i00000022-223−23−2323002-2-22−2i2i2i−2i00002i−2i00002i3−2i3−1+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
χ784-44-400-2−4i4i00000022-223−23−232300-222-22i−2i−2i2i00002i−2i00002i3−2i31−3−1+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
χ794-44-400-2−4i4i00000022-2−232323−23002-2-22−2i2i2i−2i00002i−2i0000−2i32i3−1−31+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
χ804-44-400-2−4i4i00000022-2−232323−2300-222-22i−2i−2i2i00002i−2i0000−2i32i31+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
χ814-4-444-440000-44-444-4-4-4-44400000000004-4-44000000000000000000000000000000000000000000000000000000
χ824-4-444-4-200004-44-4-222-2-22200000044-4-4-22-220000000000000000-2-222-2-222000000000000000000000000000000
χ834-4-444-4-200004-44-4-222-2-222000000-4-444-22-22000000000000000022-2-222-2-2000000000000000000000000000000
χ844-4-444-4-20000-44-44-22222-2-20000000000-222-2000000002323−23−23−23−23232300000000000000000000000000000000000000
χ854-4-444-4-20000-44-44-22222-2-20000000000-222-200000000−23−2323232323−23−2300000000000000000000000000000000000000
χ864-4-44-4440000-444-44-4-4-4-4440000000000-444-4000000000000000000000000000000000000000000000000000000
χ874-4-44-44-200004-4-44-222-2-2220044-4-400002-22-200000000-2-222-2-22200000000000000000000000000000000000000
χ884-4-44-44-200004-4-44-222-2-22200-4-44400002-22-20000000022-2-222-2-200000000000000000000000000000000000000
χ894-4-44-44-20000-444-4-22222-2-200000000002-2-2200000000000000002323−23−23−23−232323000000000000000000000000000000
χ904-4-44-44-20000-444-4-22222-2-200000000002-2-220000000000000000−23−2323232323−23−23000000000000000000000000000000

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