Finite Group Databasebeta

← Group #10944196

Character table — Group #10944196

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order122222344444466612121212224444444446612121212121244446612121212121212121212121212121212222222444444444488242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-111-1-11-1-1-1-1111111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-111-1-11-1-1-1-1111111111111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111-1-111-1-11-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111
χ811111111111111111111-1-111-1-11-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1
χ9111111111-1-111111111111-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-11-111-1-11-11-1
χ10111111111-1-111111111111-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1111-111-1-1-11-11
χ11111111111-1-111111111111-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-11-1-111-11-11
χ12111111111-1-111111111111-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-11-1-1111-11-1
χ13111111111-1-1111111111-1-1-1-111-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-111-11-1-1111-1-11
χ14111111111-1-1111111111-1-1-1-111-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-11-1-111-111-1
χ15111111111-1-1111111111-1-1-1-111-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1111-111-1-1-111-1
χ16111111111-1-1111111111-1-1-1-111-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111111-1-11-111-1-11-1-11
χ172222222-2-222-2-2222-2-2-2-200-2-2002000022-2-222-2-20000002-20000000000000022-2-2000022-2-200000000000000
χ182222222-2-222-2-2222-2-2-2-200-2-2002000022-2-222-2-20000002-200000000000000-2-2220000-2-22200000000000000
χ192222222-2-2-2-2-2-2222-2-2-2-2002200-2000022-2-2-2-222000000-220000000000000022-2-20000-2-22200000000000000
χ202222222-2-2-2-2-2-2222-2-2-2-2002200-2000022-2-2-2-222000000-2200000000000000-2-222000022-2-200000000000000
χ21222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ22222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ23222222-1222222-1-1-1-1-1-1-1-2-222-2-22-2-2-2-2-1-1-1-1-1-1-1-1222211-1-1111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ24222222-1222222-1-1-1-1-1-1-1-2-222-2-22-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-211-1-111111111111111000000000000000022-1-1-1-10000
χ25222222-122-2-222-1-1-1-1-1-1-122-2-2-2-2-222-2-2-1-1-1-1111122-2-2-1-111-1-11111-1-1-1-1111100000000000000002-2-1-1110000
χ26222222-122-2-222-1-1-1-1-1-1-122-2-2-2-2-222-2-2-1-1-1-11111-2-222-1-111-1-111111111-1-1-1-10000000000000000-2211-1-10000
χ27222222-122-2-222-1-1-1-1-1-1-1-2-2-2-222-2-2-222-1-1-1-1111122-2-2111111-1-1-1-1-1-1-1-111110000000000000000-2211-1-10000
χ28222222-122-2-222-1-1-1-1-1-1-1-2-2-2-222-2-2-222-1-1-1-11111-2-222111111-1-1-1-11111-1-1-1-100000000000000002-2-1-1110000
χ292222-2-222-2222-22222222002-200-20000-2-2-2-22222000000-2-200000000000000000022-2-20000-2-2220000000000
χ302222-2-222-2222-22222222002-200-20000-2-2-2-22222000000-2-2000000000000000000-2-222000022-2-20000000000
χ312222-2-222-2-2-22-2222222200-220020000-2-2-2-2-2-2-2-20000002200000000000000000022220000-2-2-2-20000000000
χ322222-2-222-2-2-22-2222222200-220020000-2-2-2-2-2-2-2-200000022000000000000000000-2-2-2-2000022220000000000
χ332222-2-22-2222-22222-2-2-2-222-22-2-2-2-2-222-2-22222-2-2000022-22-2-222-2-20000000000000000000000000000000000
χ342222-2-22-2222-22222-2-2-2-2-2-2-2222-222-2-2-2-22222-2-20000-2-2-2222-2-2220000000000000000000000000000000000
χ352222-2-22-22-2-2-22222-2-2-2-2222-2222-2-2-2-2-2-222-2-2220000222-2-2-2-2-2220000000000000000000000000000000000
χ362222-2-22-22-2-2-22222-2-2-2-2-2-22-2-2-222222-2-222-2-2220000-2-22-22222-2-20000000000000000000000000000000000
χ372222-2-2-1-2222-22-1-1-1111122-22-2-2-2-2-22211-1-1-1-1110000-1-11-111-1-11133−3−333−3−30000000000000000003−33−30000
χ382222-2-2-1-2222-22-1-1-1111122-22-2-2-2-2-22211-1-1-1-1110000-1-11-111-1-111−3−333−3−333000000000000000000−33−330000
χ392222-2-2-1-2222-22-1-1-11111-2-2-2222-222-2-211-1-1-1-1110000111-1-1-111-1-133−3−333−3−3000000000000000000−33−330000
χ402222-2-2-1-2222-22-1-1-11111-2-2-2222-222-2-211-1-1-1-1110000111-1-1-111-1-1−3−333−3−3330000000000000000003−33−30000
χ412222-2-2-1-22-2-2-22-1-1-11111222-2222-2-2-2-211-1-111-1-10000-1-1-111111-1-133−3−3−3−3330000000000000000003−3−330000
χ422222-2-2-1-22-2-2-22-1-1-11111222-2222-2-2-2-211-1-111-1-10000-1-1-111111-1-1−3−33333−3−3000000000000000000−333−30000
χ432222-2-2-1-22-2-2-22-1-1-11111-2-22-2-2-22222211-1-111-1-1000011-11-1-1-1-11133−3−3−3−333000000000000000000−333−30000
χ442222-2-2-1-22-2-2-22-1-1-11111-2-22-2-2-22222211-1-111-1-1000011-11-1-1-1-111−3−33333−3−30000000000000000003−3−330000
χ452-22-22-222-200-222-2-222-2-22-2000002-2002-22-2000000002-2002-20000000000000000002i−2i2i−2i2i−2i002i−2i0000000000
χ462-22-22-222-200-222-2-222-2-22-2000002-2002-22-2000000002-2002-2000000000000000000−2i2i−2i2i−2i2i00−2i2i0000000000
χ472-22-22-222-200-222-2-222-2-2-2200000-22002-22-200000000-2200-220000000000000000002i−2i−2i2i−2i2i002i−2i0000000000
χ482-22-22-222-200-222-2-222-2-2-2200000-22002-22-200000000-2200-22000000000000000000−2i2i2i−2i2i−2i00−2i2i0000000000
χ492-22-22-22-22002-22-2-2-2-22200002i−2i0002i−2i2-2-22000000000000002i−2i2i−2i0000000000002-2002i−2i−2i2i2-2000000000000
χ502-22-22-22-22002-22-2-2-2-22200002i−2i0002i−2i2-2-22000000000000002i−2i2i−2i000000000000-2200−2i2i2i−2i-22000000000000
χ512-22-22-22-22002-22-2-2-2-2220000−2i2i000−2i2i2-2-2200000000000000−2i2i−2i2i0000000000002-200−2i2i2i−2i2-2000000000000
χ522-22-22-22-22002-22-2-2-2-2220000−2i2i000−2i2i2-2-2200000000000000−2i2i−2i2i000000000000-22002i−2i−2i2i-22000000000000
χ532-22-2-2222200-2-22-2-222-2-200002i−2i000−2i2i-22-2200000000000000−2i2i2i−2i000000002-22-2002i−2i000000−2i2i0000000000
χ542-22-2-2222200-2-22-2-222-2-200002i−2i000−2i2i-22-2200000000000000−2i2i2i−2i00000000-22-2200−2i2i0000002i−2i0000000000
χ552-22-2-2222200-2-22-2-222-2-20000−2i2i0002i−2i-22-22000000000000002i−2i−2i2i000000002-22-200−2i2i0000002i−2i0000000000
χ562-22-2-2222200-2-22-2-222-2-20000−2i2i0002i−2i-22-22000000000000002i−2i−2i2i00000000-22-22002i−2i000000−2i2i0000000000
χ572-22-2-222-2-200222-2-2-2-2222-200000-2200-222-2000000002-200-220000000000002-2-222-2000000-22000000000000
χ582-22-2-222-2-200222-2-2-2-2222-200000-2200-222-2000000002-200-22000000000000-222-2-220000002-2000000000000
χ592-22-2-222-2-200222-2-2-2-222-22000002-200-222-200000000-22002-20000000000002-2-22-220000002-2000000000000
χ602-22-2-222-2-200222-2-2-2-222-22000002-200-222-200000000-22002-2000000000000-222-22-2000000-22000000000000
χ61444444-2-4-444-4-4-2-2-2222200-4-40040000-2-222-2-222000000-220000000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-4-2-2-22222004400-40000-2-22222-2-20000002-20000000000000000000000000000000000000000
χ634444-4-4-24-4444-4-2-2-2-2-2-2-2004-400-400002222-2-2-2-2000000220000000000000000000000000000000000000000
χ644444-4-4-24-4-4-44-4-2-2-2-2-2-2-200-44004000022222222000000-2-20000000000000000000000000000000000000000
χ6544-4-4004004i−4i00-44-400000000000000000004i−4i002-22i−2i00000000002-22-22i−2i2i−2i00000000000000000000000000
χ6644-4-4004004i−4i00-44-400000000000000000004i−4i00-22−2i2i0000000000-22-22−2i2i−2i2i00000000000000000000000000
χ6744-4-400400−4i4i00-44-40000000000000000000−4i4i002-2−2i2i00000000002-22-2−2i2i−2i2i00000000000000000000000000
χ6844-4-400400−4i4i00-44-40000000000000000000−4i4i00-222i−2i0000000000-22-222i−2i2i−2i00000000000000000000000000
χ6944-4-400-2004i−4i002-2223−2323−23000000000000000−2i2i−2i32i32-22i−2i0000000000−1+31−3−1−31+3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000000
χ7044-4-400-2004i−4i002-2223−2323−23000000000000000−2i2i−2i32i3-22−2i2i00000000001−3−1+31+3−1−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000000
χ7144-4-400-2004i−4i002-22−2323−2323000000000000000−2i2i2i3−2i32-22i−2i0000000000−1−31+3−1+31−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000000
χ7244-4-400-2004i−4i002-22−2323−2323000000000000000−2i2i2i3−2i3-22−2i2i00000000001+3−1−31−3−1+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000000
χ7344-4-400-200−4i4i002-2223−2323−230000000000000002i−2i2i3−2i32-2−2i2i0000000000−1+31−3−1−31+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000000
χ7444-4-400-200−4i4i002-2223−2323−230000000000000002i−2i2i3−2i3-222i−2i00000000001−3−1+31+3−1−3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000000
χ7544-4-400-200−4i4i002-22−2323−23230000000000000002i−2i−2i32i32-2−2i2i0000000000−1−31+3−1+31−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000000
χ7644-4-400-200−4i4i002-22−2323−23230000000000000002i−2i−2i32i3-222i−2i00000000001+3−1−31−3−1+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000000
χ774-44-44-4-24-400-44-222-2-2224-4000004-400-22-2200000000-2200-2200000000000000000000000000000000000000
χ784-44-44-4-24-400-44-222-2-222-4400000-4400-22-22000000002-2002-200000000000000000000000000000000000000
χ794-44-44-4-2-44004-4-22222-2-200004i−4i0004i−4i-222-200000000000000−2i2i−2i2i0000000000000000000000000000000000
χ804-44-44-4-2-44004-4-22222-2-20000−4i4i000−4i4i-222-2000000000000002i−2i2i−2i0000000000000000000000000000000000
χ814-44-4-44-24400-4-4-222-2-22200004i−4i000−4i4i2-22-2000000000000002i−2i−2i2i0000000000000000000000000000000000
χ824-44-4-44-24400-4-4-222-2-2220000−4i4i0004i−4i2-22-200000000000000−2i2i2i−2i0000000000000000000000000000000000
χ834-44-4-44-2-4-40044-22222-2-24-400000-44002-2-2200000000-22002-200000000000000000000000000000000000000
χ844-44-4-44-2-4-40044-22222-2-2-44000004-4002-2-22000000002-200-2200000000000000000000000000000000000000
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 12 (ζ12 = 1); i = ζ3.