Finite Group Databasebeta

← Group #11776167

Character table — Group #11776167

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size11112222222222222222444444444444444444444444444121212121212121212121212242424242424363636361111222222222222222244444444444444444444444444412121212121212121212121224242424242436363636
order1222334444666666121212123466612121212121212121212121212121212121212121212888824242424242424244412121212888822226644446666661212121264666121212121212121212121212121212121212121212128888242424242424242444121212128888
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
χ5111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1-111-1-1ii−i−i111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1-111-1-1ii−i−i
χ6111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-11-1-111−i−iii111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-11-1-111−i−iii
χ7111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1-111-1-1−i−iii111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1-111-1-1−i−iii
χ8111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-11-1-111ii−i−i111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-11-1-111ii−i−i
χ92222222-22-222222222222-2222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000002222222-22-222222222222-2222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000
χ10222222-22-22222222-2-2-2-22-2222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222220000000000000000000000222222-22-22222222-2-2-2-22-2222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222220000000000000000000000
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χ1222222-12222222-1-1-12222-12-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-21111000022222-12222222-1-1-12222-12-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-211110000
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χ1422222-12-22-2222-1-1-12222-1-2-1-1-1-2-2-1-1-2-211111111-1-1-1-1111100000000000000i3−i3i3−i3000022222-12-22-2222-1-1-12222-1-2-1-1-1-2-2-1-1-2-211111111-1-1-1-1111100000000000000i3−i3i3−i30000
χ1522222-1-22-22222-1-1-1-2-2-2-2-1-2-1-1-1-2-21122-1-11111111111-1-1-1-100000000000000−i3i3i3−i3000022222-1-22-22222-1-1-1-2-2-2-2-1-2-1-1-1-2-21122-1-11111111111-1-1-1-100000000000000−i3i3i3−i30000
χ1622222-1-22-22222-1-1-1-2-2-2-2-1-2-1-1-1-2-21122-1-11111111111-1-1-1-100000000000000i3−i3−i3i3000022222-1-22-22222-1-1-1-2-2-2-2-1-2-1-1-1-2-21122-1-11111111111-1-1-1-100000000000000i3−i3−i3i30000
χ1722222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-12211-2-211-1-1-1-1-1-1111111110000000000002-2-1-111000022222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-12211-2-211-1-1-1-1-1-1111111110000000000002-2-1-1110000
χ1822222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-12211-2-211-1-1-1-1-1-111111111000000000000-2211-1-1000022222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-12211-2-211-1-1-1-1-1-111111111000000000000-2211-1-10000
χ192222-122222-1-1-1222-1-1-1-1-12-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000002222-122222-1-1-1222-1-1-1-1-12-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ202222-122222-1-1-1222-1-1-1-1-12-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000002222-122222-1-1-1222-1-1-1-1-12-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ212222-122-22-2-1-1-1222-1-1-1-1-1-2-1-1-1112211-2-2-2-21111-1-1-1-111110000−i3−i3i3i3−i3−i3i3i300000000002222-122-22-2-1-1-1222-1-1-1-1-1-2-1-1-1112211-2-2-2-21111-1-1-1-111110000−i3−i3i3i3−i3−i3i3i30000000000
χ222222-122-22-2-1-1-1222-1-1-1-1-1-2-1-1-1112211-2-2-2-21111-1-1-1-111110000i3i3−i3−i3i3i3−i3−i300000000002222-122-22-2-1-1-1222-1-1-1-1-1-2-1-1-1112211-2-2-2-21111-1-1-1-111110000i3i3−i3−i3i3i3−i3−i30000000000
χ232222-12-22-22-1-1-12221111-1-2-1-1-111-2-2-1-122-2-211111111-1-1-1-1000033−3−3−3−33300000000002222-12-22-22-1-1-12221111-1-2-1-1-111-2-2-1-122-2-211111111-1-1-1-1000033−3−3−3−3330000000000
χ242222-12-22-22-1-1-12221111-1-2-1-1-111-2-2-1-122-2-211111111-1-1-1-10000−3−33333−3−300000000002222-12-22-22-1-1-12221111-1-2-1-1-111-2-2-1-122-2-211111111-1-1-1-10000−3−33333−3−30000000000
χ252222-12-2-2-2-2-1-1-12221111-12-1-1-1-1-1-2-211-2-222-1-1-1-1111111112i2i−2i−2i−i−i−i−iiiii00000000002222-12-2-2-2-2-1-1-12221111-12-1-1-1-1-1-2-211-2-222-1-1-1-1111111112i2i−2i−2i−i−i−i−iiiii0000000000
χ262222-12-2-2-2-2-1-1-12221111-12-1-1-1-1-1-2-211-2-222-1-1-1-111111111−2i−2i2i2iiiii−i−i−i−i00000000002222-12-2-2-2-2-1-1-12221111-12-1-1-1-1-1-2-211-2-222-1-1-1-111111111−2i−2i2i2iiiii−i−i−i−i0000000000
χ2722-2-222020-22-2-22-2-20000202-2-200002-22-2000000000022-2-22−22−22−22−22−22−2000000000022-2-222020-22-2-22-2-20000202-2-200002-22-2000000000022-2-22−22−22−22−22−22−20000000000
χ2822-2-222020-22-2-22-2-20000202-2-200002-22-2000000000022-2-2−22−22−22−22−22−22000000000022-2-222020-22-2-22-2-20000202-2-200002-22-2000000000022-2-2−22−22−22−22−22−220000000000
χ2922-2-2220-2022-2-22-2-20000202-2-20000-22-220000000000-2-222−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000022-2-2220-2022-2-22-2-20000202-2-20000-22-220000000000-2-222−i2i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ3022-2-2220-2022-2-22-2-20000202-2-20000-22-220000000000-2-222i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000022-2-2220-2022-2-22-2-20000202-2-20000-22-220000000000-2-222i2−i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ3122-2-2-12020-2-1112-2-23−33−3-10-1113−300-112-20033−3−333−3−3-1-1112−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000022-2-2-12020-2-1112-2-23−33−3-10-1113−300-112-20033−3−333−3−3-1-1112−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ3222-2-2-12020-2-1112-2-23−33−3-10-1113−300-112-20033−3−333−3−3-1-111−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000022-2-2-12020-2-1112-2-23−33−3-10-1113−300-112-20033−3−333−3−3-1-111−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ3322-2-2-12020-2-1112-2-2−33−33-10-111−3300-112-200−3−333−3−333-1-1112−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000022-2-2-12020-2-1112-2-2−33−33-10-111−3300-112-200−3−333−3−333-1-1112−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ3422-2-2-12020-2-1112-2-2−33−33-10-111−3300-112-200−3−333−3−333-1-111−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000022-2-2-12020-2-1112-2-2−33−33-10-111−3300-112-200−3−333−3−333-1-111−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
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χ3622-2-2-120-202-1112-2-23−33−3-10-111−33001-1-2200−3−33333−3−311-1-1i2−i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000022-2-2-120-202-1112-2-23−33−3-10-111−33001-1-2200−3−33333−3−311-1-1i2−i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000
χ3722-2-2-120-202-1112-2-2−33−33-10-1113−3001-1-220033−3−3−3−33311-1-1−i2i2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000022-2-2-120-202-1112-2-2−33−33-10-1113−3001-1-220033−3−3−3−33311-1-1−i2i2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000
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χ1274-44-4-2-240-402-222-22-2-22210-11-100-22000000−3i3i−3i3i1-11-1−3i3i−3i3i0000000000000000000000-44-4422-4040-22-2-22-222-2-2-101-11002-20000003i−3i3i−3i-11-113i−3i3i−3i0000000000000000000000
χ1284-44-4-2-2-40402-222-2222-2-210-11-1002-20000003i−3i3i−3i-11-11−3i3i−3i3i0000000000000000000000-44-442240-40-22-2-22-2-2-222-101-1100-22000000−3i3i−3i3i1-11-13i−3i3i−3i0000000000000000000000
χ1294-44-4-2-2-40402-222-2222-2-210-11-1002-2000000−3i3i−3i3i-11-113i−3i3i−3i0000000000000000000000-44-442240-40-22-2-22-2-2-222-101-1100-220000003i−3i3i−3i1-11-1−3i3i−3i3i0000000000000000000000
χ1304-4-44440000-4-44-4-44000040-4-4400000000000000000000000000000000000000000000-444-4-4-4000044-444-40000-4044-400000000000000000000000000000000000000000000
χ1314-4-444-20000-4-4422-20000-2022-200000000−2i32i3−2i32i32i3−2i3000000000000000000000000000000-444-4-42000044-4-2-22000020-2-22000000002i3−2i32i3−2i3−2i32i3000000000000000000000000000000
χ1324-4-444-20000-4-4422-20000-2022-2000000002i3−2i32i3−2i3−2i32i3000000000000000000000000000000-444-4-42000044-4-2-22000020-2-2200000000−2i32i3−2i32i32i3−2i3000000000000000000000000000000
χ1334-4-44-24000022-2-4-4423−23−2323-2022-20000000000000023−23−232300000000000000000000000000-444-42-40000-2-2244-4−232323−2320-2-2200000000000000−232323−2300000000000000000000000000
χ1344-4-44-24000022-2-4-44−232323−23-2022-200000000000000−232323−2300000000000000000000000000-444-42-40000-2-2244-423−23−232320-2-220000000000000023−23−232300000000000000000000000000
χ1354-4-44-2-2000022-222-223−23−232310-1-1100000000−2i32i3i3−i3−i3i3−333−33i−3i−3i3i0000000000000000000000-444-4220000-2-22-2-22−232323−23-1011-1000000002i3−2i3−i3i3i3−i33−3−33−3i3i3i−3i0000000000000000000000
χ1364-4-44-2-2000022-222-223−23−232310-1-11000000002i3−2i3−i3i3i3−i3−333−3−3i3i3i−3i0000000000000000000000-444-4220000-2-22-2-22−232323−23-1011-100000000−2i32i3i3−i3−i3i33−3−333i−3i−3i3i0000000000000000000000
χ1374-4-44-2-2000022-222-2−232323−2310-1-1100000000−2i32i3i3−i3−i3i33−3−33−3i3i3i−3i0000000000000000000000-444-4220000-2-22-2-2223−23−2323-1011-1000000002i3−2i3−i3i3i3−i3−333−33i−3i−3i3i0000000000000000000000
χ1384-4-44-2-2000022-222-2−232323−2310-1-11000000002i3−2i3−i3i3i3−i33−3−333i−3i−3i3i0000000000000000000000-444-4220000-2-22-2-2223−23−2323-1011-100000000−2i32i3i3−i3−i3i3−333−3−3i3i3i−3i0000000000000000000000

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