Finite Group Databasebeta

← Group #11868454

Character table — Group #11868454

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size11112222222222222222444444444444444444444444444121212121212121212121212242424242424363636361111222222222222222244444444444444444444444444412121212121212121212121224242424242436363636
order1222334444666666121212123466612121212121212121212121212121212121212121212888824242424242424244412121212444422226644446666661212121264666121212121212121212121212121212121212121212128888242424242424242444121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-11111111111111-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-1111111-1-11111111111111-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-1
χ6111111-1-11111111111111-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-111111111-1-11111111111111-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-111
χ7111111-1-11111111111111-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-111-1-1-1-111111111-1-11111111111111-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-111-1-1-1-111
χ8111111-1-11111111111111-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-1111111-1-11111111111111-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-1
χ922222222-2-2222222-2-2-2-22-2222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000022222222-2-2222222-2-2-2-22-2222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000
χ10222222-2-2-2-2222222-2-2-2-222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000222222-2-2-2-2222222-2-2-2-222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000
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χ1422222-122-2-2222-1-1-1-2-2-2-2-1-2-1-1-11122-1-1-2-2111111-1-1-1-1111100000000000000i3−i3i3−i3000022222-122-2-2222-1-1-1-2-2-2-2-1-2-1-1-11122-1-1-2-2111111-1-1-1-1111100000000000000i3−i3i3−i30000
χ1522222-1-2-222222-1-1-12222-1-2-1-1-1-1-1-2-211-2-211-1-1-1-1111111110000000000002-2-1-111000022222-1-2-222222-1-1-12222-1-2-1-1-1-1-1-2-211-2-211-1-1-1-1111111110000000000002-2-1-1110000
χ1622222-1-2-222222-1-1-12222-1-2-1-1-1-1-1-2-211-2-211-1-1-1-111111111000000000000-2211-1-1000022222-1-2-222222-1-1-12222-1-2-1-1-1-1-1-2-211-2-211-1-1-1-111111111000000000000-2211-1-10000
χ1722222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-111-2-21122-1-111111111-1-1-1-100000000000000−i3i3i3−i3000022222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-111-2-21122-1-111111111-1-1-1-100000000000000−i3i3i3−i30000
χ1822222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-111-2-21122-1-111111111-1-1-1-100000000000000i3−i3−i3i3000022222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-111-2-21122-1-111111111-1-1-1-100000000000000i3−i3−i3i30000
χ192222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000002222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ202222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000002222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ212222-1222-2-2-1-1-12221111-1-2-1-1-1-2-2-1-12211-2-21111-1-1-1-11111000033−3−333−3−300000000002222-1222-2-2-1-1-12221111-1-2-1-1-1-2-2-1-12211-2-21111-1-1-1-11111000033−3−333−3−30000000000
χ222222-1222-2-2-1-1-12221111-1-2-1-1-1-2-2-1-12211-2-21111-1-1-1-111110000−3−333−3−33300000000002222-1222-2-2-1-1-12221111-1-2-1-1-1-2-2-1-12211-2-21111-1-1-1-111110000−3−333−3−3330000000000
χ232222-12-2-222-1-1-1222-1-1-1-1-1-2-1-1-12211-2-211-2-2-1-1-1-11111111122-2-2-1-1-1-1111100000000002222-12-2-222-1-1-1222-1-1-1-1-1-2-1-1-12211-2-211-2-2-1-1-1-11111111122-2-2-1-1-1-111110000000000
χ242222-12-2-222-1-1-1222-1-1-1-1-1-2-1-1-12211-2-211-2-2-1-1-1-111111111-2-2221111-1-1-1-100000000002222-12-2-222-1-1-1222-1-1-1-1-1-2-1-1-12211-2-211-2-2-1-1-1-111111111-2-2221111-1-1-1-10000000000
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χ262222-12-2-2-2-2-1-1-12221111-12-1-1-1-2-211-2-2-1-12211111111-1-1-1-10000−3−33333−3−300000000002222-12-2-2-2-2-1-1-12221111-12-1-1-1-2-211-2-2-1-12211111111-1-1-1-10000−3−33333−3−30000000000
χ2722-2-2222-2002-2-22-2-20000202-2-2002-22-20000000022-2-200002−22−22−22−22−22−2000000000022-2-2222-2002-2-22-2-20000202-2-2002-22-20000000022-2-200002−22−22−22−22−22−20000000000
χ2822-2-2222-2002-2-22-2-20000202-2-2002-22-20000000022-2-20000−22−22−22−22−22−22000000000022-2-2222-2002-2-22-2-20000202-2-2002-22-20000000022-2-20000−22−22−22−22−22−220000000000
χ2922-2-222-22002-2-22-2-20000202-2-200-22-2200000000-2-22200002−2−222−22−2−22−22000000000022-2-222-22002-2-22-2-20000202-2-200-22-2200000000-2-22200002−2−222−22−2−22−220000000000
χ3022-2-222-22002-2-22-2-20000202-2-200-22-2200000000-2-2220000−222−2−22−222−22−2000000000022-2-222-22002-2-22-2-20000202-2-200-22-2200000000-2-2220000−222−2−22−222−22−20000000000
χ3122-2-2-122-200-1112-2-23−33−3-10-11100-112-23−30033−3−3-1-11133−3−32−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000022-2-2-122-200-1112-2-23−33−3-10-11100-112-23−30033−3−3-1-11133−3−32−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ3222-2-2-122-200-1112-2-23−33−3-10-11100-112-23−30033−3−3-1-11133−3−3−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000022-2-2-122-200-1112-2-23−33−3-10-11100-112-23−30033−3−3-1-11133−3−3−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ3322-2-2-122-200-1112-2-2−33−33-10-11100-112-2−3300−3−333-1-111−3−3332−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000022-2-2-122-200-1112-2-2−33−33-10-11100-112-2−3300−3−333-1-111−3−3332−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
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χ3522-2-2-12-2200-1112-2-23−33−3-10-111001-1-22−330033−3−311-1-1−3−3332−2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000022-2-2-12-2200-1112-2-23−33−3-10-111001-1-22−330033−3−311-1-1−3−3332−2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
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χ3822-2-2-12-2200-1112-2-2−33−33-10-111001-1-223−300−3−33311-1-133−3−3−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000022-2-2-12-2200-1112-2-2−33−33-10-111001-1-223−300−3−33311-1-133−3−3−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
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χ1314-4-444-20000-4-4422-20000-2022-200000000−2i32i300000000−2i32i32i3−2i30000000000000000000000-444-4-42000044-4-2-22000020-2-22000000002i3−2i3000000002i3−2i3−2i32i30000000000000000000000
χ1324-4-444-20000-4-4422-20000-2022-2000000002i3−2i3000000002i3−2i3−2i32i30000000000000000000000-444-4-42000044-4-2-22000020-2-2200000000−2i32i300000000−2i32i32i3−2i30000000000000000000000
χ1334-4-44-24000022-2-4-4423−23−2323-2022-2000000000023−23−2323000000000000000000000000000000-444-42-40000-2-2244-4−232323−2320-2-220000000000−232323−23000000000000000000000000000000
χ1344-4-44-24000022-2-4-44−232323−23-2022-20000000000−232323−23000000000000000000000000000000-444-42-40000-2-2244-423−23−232320-2-22000000000023−23−2323000000000000000000000000000000
χ1354-4-44-2-2000022-222-223−23−232310-1-1100000000−2i32i3−333−33i−3i−3i3ii3−i3−i3i30000000000000000000000-444-4220000-2-22-2-22−232323−23-1011-1000000002i3−2i33−3−33−3i3i3i−3i−i3i3i3−i30000000000000000000000
χ1364-4-44-2-2000022-222-223−23−232310-1-11000000002i3−2i3−333−3−3i3i3i−3i−i3i3i3−i30000000000000000000000-444-4220000-2-22-2-22−232323−23-1011-100000000−2i32i33−3−333i−3i−3i3ii3−i3−i3i30000000000000000000000
χ1374-4-44-2-2000022-222-2−232323−2310-1-1100000000−2i32i33−3−33−3i3i3i−3ii3−i3−i3i30000000000000000000000-444-4220000-2-22-2-2223−23−2323-1011-1000000002i3−2i3−333−33i−3i−3i3i−i3i3i3−i30000000000000000000000
χ1384-4-44-2-2000022-222-2−232323−2310-1-11000000002i3−2i33−3−333i−3i−3i3i−i3i3i3−i30000000000000000000000-444-4220000-2-22-2-2223−23−2323-1011-100000000−2i32i3−333−3−3i3i3i−3ii3−i3−i3i30000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.