Finite Group Databasebeta

← Group #72341933

Character table — Group #72341933

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size112222244444666612121212121212121212121212121212121212121212121212121212121212121212121212121616161632323232323232323232323232326464646464646464646496969696128128128128128128128128
order122448881616161622442222444488888888881616161616161616161616161616161616161616336622246612121212242424242424484848484848484844446666661212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32
χ4111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321−i321−i321−i321+i321−i32
χ5111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32
χ6111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321+i321+i321+i321−i321+i32
χ711111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111111111-1-1-1-1-1-1-1-111-1-111-111-1-1-1
χ811111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-1111
χ911111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1−i321+i32−1+i32−1+i321−i321+i321−i32
χ1011111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1111+i321+i32−1−i321−i321−i32−1+i32−1−i32−1+i32
χ1111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1+i321−i32−1−i32−1−i321+i321−i321+i32
χ1211111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1111−i321−i32−1+i321+i321+i32−1−i32−1+i32−1−i32
χ1311-1-1111-111-1-1-111-111-1-111-1-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111-11-1-1-1-1-1111111-1-111-1-111-1-11-11-11-111-11-1-1
χ1411-1-1111-111-1-1-111-111-1-111-1-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-11-11-1-1-1-1111111-1-111-1-111-1-1-11-11-11-1-11-111
χ1511-1-1111-111-1-1-111-111-1-111-1-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321-11-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-11-1−1−i321+i32−1−i32−1+i321−i32−1+i321+i321−i32
χ1611-1-1111-111-1-1-111-111-1-111-1-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32-11-111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-11-111+i32−1−i321+i321−i32−1+i321−i32−1−i32−1+i32
χ1711-1-1111-111-1-1-111-111-1-111-1-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321-11-11−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-11-1−1+i321−i32−1+i32−1−i321+i32−1−i321−i321+i32
χ1811-1-1111-111-1-1-111-111-1-111-1-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32-11-111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-11-111−i32−1+i321−i321+i32−1−i321+i32−1+i32−1−i32
χ1911-1-1111-1-1-111-111-111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-11-1-1-1-1111111-1-1-1-111-1-1111-1-111-1-11-1-111
χ2011-1-1111-1-1-111-111-111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-111-1-1-1-1-1111111-1-1-1-111-1-111-111-1-111-111-1-1
χ2111-1-1111-1-1-111-111-111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−1−i32−1+i32−1−i32−1+i321-1-111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1-11−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i32
χ2211-1-1111-1-1-111-111-111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−1−i32−1+i32−1−i32−1+i32-111-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111-11+i32−1−i32−1−i321−i32−1+i32−1+i321+i321−i32
χ2311-1-1111-1-1-111-111-111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−1+i32−1−i32−1+i32−1−i321-1-111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1-11−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i32
χ2411-1-1111-1-1-111-111-111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−1+i32−1−i32−1+i32−1−i32-111-11−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111-11−i32−1+i32−1+i321+i32−1−i32−1−i321−i321+i32
χ2522222-2-2-20000222222222222-2-2-2-2-2-2-2-2-2-20000000000000000000022220000222222-2-2-2-2-2-200000000000000000000
χ2622222-2-2-20000222222222222-2-2-2-2-2-2-2-2-2-200000000000000000000−1−i3−1+i3−1−i3−1+i30000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i31+i31−i300000000000000000000
χ2722222-2-2-20000222222222222-2-2-2-2-2-2-2-2-2-200000000000000000000−1+i3−1−i3−1+i3−1−i30000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i31−i31+i300000000000000000000
χ28222-2-20002−22−222-2-22-22-22-22-2000000000022222−2−2−2−2−222222−2−2−2−2−22222000022-2-2-2-20000002−22−22−22−2000000000000
χ29222-2-20002−22−222-2-22-22-22-22-2000000000022222−2−2−2−2−222222−2−2−2−2−2−1−i3−1+i3−1−i3−1+i30000−1−i3−1+i31+i31−i31+i31−i3000000−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ23000000000000
χ30222-2-20002−22−222-2-22-22-22-22-2000000000022222−2−2−2−2−222222−2−2−2−2−2−1+i3−1−i3−1+i3−1−i30000−1+i3−1−i31−i31+i31−i31+i3000000ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ13000000000000
χ31222-2-2000−22−2222-2-22-22-22-22-20000000000−2−2−2−2−222222−2−2−2−2−2222222222000022-2-2-2-2000000−22−22−22−22000000000000
χ32222-2-2000−22−2222-2-22-22-22-22-20000000000−2−2−2−2−222222−2−2−2−2−222222−1−i3−1+i3−1−i3−1+i30000−1−i3−1+i31+i31−i31+i31−i3000000ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ23000000000000
χ33222-2-2000−22−2222-2-22-22-22-22-20000000000−2−2−2−2−222222−2−2−2−2−222222−1+i3−1−i3−1+i3−1−i30000−1+i3−1−i31−i31+i31−i31+i3000000−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ13000000000000
χ3422-22-20002−2−22-22-222-2-222-2-22000000000022222−2−2−2−2−2−2−2−2−2−22222222220000-2-222-2-20000002−2−222−2−22000000000000
χ3522-22-20002−2−22-22-222-2-222-2-22000000000022222−2−2−2−2−2−2−2−2−2−222222−1−i3−1+i3−1−i3−1+i300001+i31−i3−1−i3−1+i31+i31−i3000000−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23000000000000
χ3622-22-20002−2−22-22-222-2-222-2-22000000000022222−2−2−2−2−2−2−2−2−2−222222−1+i3−1−i3−1+i3−1−i300001−i31+i3−1+i3−1−i31−i31+i3000000ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13000000000000
χ3722-22-2000−222−2-22-222-2-222-2-220000000000−2−2−2−2−22222222222−2−2−2−2−222220000-2-222-2-2000000−222−2−222−2000000000000
χ3822-22-2000−222−2-22-222-2-222-2-220000000000−2−2−2−2−22222222222−2−2−2−2−2−1−i3−1+i3−1−i3−1+i300001+i31−i3−1−i3−1+i31+i31−i3000000ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23000000000000
χ3922-22-2000−222−2-22-222-2-222-2-220000000000−2−2−2−2−22222222222−2−2−2−2−2−1+i3−1−i3−1+i3−1−i300001−i31+i3−1+i3−1−i31−i31+i3000000−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13000000000000
χ4022-2-22-2-220000-222-222-2-222-2-2-2-2-2-2-2222220000000000000000000022220000-2-2-2-222-2-2-2-22200000000000000000000
χ4122-2-22-2-220000-222-222-2-222-2-2-2-2-2-2-22222200000000000000000000−1−i3−1+i3−1−i3−1+i300001+i31−i31+i31−i3−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i300000000000000000000
χ4222-2-22-2-220000-222-222-2-222-2-2-2-2-2-2-22222200000000000000000000−1+i3−1−i3−1+i3−1−i300001−i31+i31−i31+i3−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i300000000000000000000
χ433333333333333333-1-1-1-1-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-10000333300000000000000000000-1-1-1-100000000
χ443333333333333333-1-1-1-1-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-10000-3-3-3-300000000000000000000111100000000
χ4533333333-3-3-3-33333-1-1-1-1-1-1-1-13-1-1-1-13-1-1-1-1-31111-31111-31111-31111000033-3-300000000000000000000-1-11100000000
χ4633333333-3-3-3-33333-1-1-1-1-1-1-1-13-1-1-1-13-1-1-1-1-31111-31111-31111-311110000-3-3330000000000000000000011-1-100000000
χ4733-3-3333-333-3-3-333-3-1-111-1-1113-1-1-1-1-311113-1-1-1-13-1-1-1-1-31111-3111100003-33-300000000000000000000-11-1100000000
χ4833-3-3333-333-3-3-333-3-1-111-1-1113-1-1-1-1-311113-1-1-1-13-1-1-1-1-31111-311110000-33-33000000000000000000001-11-100000000
χ4933-3-3333-3-3-333-333-3-1-111-1-1113-1-1-1-1-31111-31111-311113-1-1-1-13-1-1-1-100003-3-3300000000000000000000-111-100000000
χ5033-3-3333-3-3-333-333-3-1-111-1-1113-1-1-1-1-31111-31111-311113-1-1-1-13-1-1-1-10000-333-3000000000000000000001-1-1100000000
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χ60666-6-600032−3232−3266-6-6-22-22-22-22000000000032−2−2−2−2−32222232−2−2−2−2−3222220000000000000000000000000000000000000000
χ61666-6-600032−3232−32-2-2222222-2-2-2-204i−4i0004i−4i00−2−3ζ5−ζ7−3ζ13−ζ23ζ5+3ζ7+ζ13+3ζ23−2−223ζ5+ζ7+3ζ13+ζ23−ζ5−3ζ7−ζ13−3ζ2322−2−3ζ5−ζ7−3ζ13−ζ23ζ5+3ζ7+ζ13+3ζ23−2−223ζ5+ζ7+3ζ13+ζ23−ζ5−3ζ7−ζ13−3ζ23220000000000000000000000000000000000000000
χ62666-6-600032−3232−32-2-2222222-2-2-2-20−4i4i000−4i4i00−2ζ5+3ζ7+ζ13+3ζ23−3ζ5−ζ7−3ζ13−ζ23−2−22−ζ5−3ζ7−ζ13−3ζ233ζ5+ζ7+3ζ13+ζ2322−2ζ5+3ζ7+ζ13+3ζ23−3ζ5−ζ7−3ζ13−ζ23−2−22−ζ5−3ζ7−ζ13−3ζ233ζ5+ζ7+3ζ13+ζ23220000000000000000000000000000000000000000
χ63666-6-600032−3232−32-2-222-2-2-2-222220004i−4i0004i−4i−2−2−2−3ζ5−ζ7−3ζ13−ζ23ζ5+3ζ7+ζ13+3ζ232223ζ5+ζ7+3ζ13+ζ23−ζ5−3ζ7−ζ13−3ζ23−2−2−2−3ζ5−ζ7−3ζ13−ζ23ζ5+3ζ7+ζ13+3ζ232223ζ5+ζ7+3ζ13+ζ23−ζ5−3ζ7−ζ13−3ζ230000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.