Finite Group Databasebeta

← Group #11776250

Character table — Group #11776250

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222244444444444444444444444488881212121212121212121212121212121212121212121212121818181824242424242424242424242436363636363636363636
order12224444444433666666121212121212121212121212121212121212121288888888242424242424242424242424242424244444444412121212121212122488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ511111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111-1-11111-1-1-1-111iiii−i−i−i−i
χ611111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-111-1-1-1-1111111−i−i−i−iiiii
χ711111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111-1-11111-1-1-1-111−i−i−i−iiiii
χ811111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-111-1-1-1-1111111iiii−i−i−i−i
χ91111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11-11-111-1-111-1-1-11ii−i−iii−i−i
χ101111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1-11-11-1-111-1-111-11−i−iii−i−iii
χ111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-11-11-111-1-111-1-1-11−i−iii−i−iii
χ121111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1-11-11-1-111-1-111-11ii−i−iii−i−i
χ131111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111-1-1111-1-1-1-111-1111-1-1-1-111
χ141111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-111-1-1-11111-1-1-11-1-11111-1-1
χ151111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1111-1-1-1-111-11-1-11111-1-1
χ161111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1-1-11111-1-1-1111-1-1-1-111
χ172222222222222222222222222222222222222222000000000000000000000000-2-2-2-2000000000000-2-200000000
χ1822222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222000000000000-2-200000000
χ192222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2000000000000000000000000-2-2220000000000002-200000000
χ202222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000000022-2-20000000000002-200000000
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χ302-2-222i−2i2i−2i2i−2i2-222-22-2-2-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i22-2-22i−2i2-2000000000000000000000000000000000000000000i2−i2−22−22i2−i2
χ312-2-222i−2i2i−2i−2i2i-2222-22-2-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-2-222−2i2i-220000000000000000000000000000000000000000002−2i2−i2−i2i2−22
χ322-2-222i−2i2i−2i−2i2i-2222-22-2-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-2-222−2i2i-22000000000000000000000000000000000000000000−22−i2i2i2−i22−2
χ332-2-22−2i2i−2i2i2i−2i-2222-22-2-2-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-2-2222i−2i-220000000000000000000000000000000000000000002−2−i2i2i2−i2−22
χ342-2-22−2i2i−2i2i2i−2i-2222-22-2-2-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-2-2222i−2i-22000000000000000000000000000000000000000000−22i2−i2−i2i22−2
χ352-2-22−2i2i−2i2i−2i2i2-222-22-2-2-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i22-2-2−2i2i2-2000000000000000000000000000000000000000000−i2i2−22−22−i2i2
χ362-2-22−2i2i−2i2i−2i2i2-222-22-2-2-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i22-2-2−2i2i2-2000000000000000000000000000000000000000000i2−i22−22−2i2−i2
χ374444444444441-2111-2-2-21-21-21-21-211111111-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ384444444444441-2111-2-2-21-21-21-21-211111111-2-2-2-2-2-2-2-2-2-2-2-2111111111111111100000000000000000000000000
χ39444444444444-21-2-2-2111-21-21-21-21-2-2-2-2-2-2-2-2111100000000000000000000000000002222-1-1-1-1-1-1-1-10000000000
χ40444444444444-21-2-2-2111-21-21-21-21-2-2-2-2-2-2-2-211110000000000000000000000000000-2-2-2-2111111110000000000
χ4144444444-4-4-4-41-2111-2-2-21-21-21-21-2-1-1-1-1-1-1-1-122222i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii00000000000000000000000000
χ4244444444-4-4-4-41-2111-2-2-21-21-21-21-2-1-1-1-1-1-1-1-12222−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i00000000000000000000000000
χ4344444444-4-4-4-4-21-2-2-2111-21-21-21-2122222222-1-1-1-1000000000000000000000000000022-2-2-1-1-1-111110000000000
χ4444444444-4-4-4-4-21-2-2-2111-21-21-21-2122222222-1-1-1-10000000000000000000000000000-2-2221111-1-1-1-10000000000
χ454444-4-4-4-444-4-41-2111-2-2-2-12-12-12-121111-1-1-1-1-2-2222i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii00000000000000000000000000
χ464444-4-4-4-444-4-41-2111-2-2-2-12-12-12-121111-1-1-1-1-2-222−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i00000000000000000000000000
χ474444-4-4-4-444-4-4-21-2-2-21112-12-12-12-1-2-2-2-2222211-1-100000000000000000000000000002-22-2-1-111-1-1110000000000
χ484444-4-4-4-444-4-4-21-2-2-21112-12-12-12-1-2-2-2-2222211-1-10000000000000000000000000000-22-2211-1-111-1-10000000000
χ494444-4-4-4-4-4-4441-2111-2-2-2-12-12-12-12-1-1-1-1111122-2-222-2-2-2-222-1-1-1-111111111-1-1-1-100000000000000000000000000
χ504444-4-4-4-4-4-4441-2111-2-2-2-12-12-12-12-1-1-1-1111122-2-2-2-22222-2-21111-1-1-1-1-1-1-1-1111100000000000000000000000000
χ514444-4-4-4-4-4-444-21-2-2-21112-12-12-12-12222-2-2-2-2-1-11100000000000000000000000000002-2-22-1-11111-1-10000000000
χ524444-4-4-4-4-4-444-21-2-2-21112-12-12-12-12222-2-2-2-2-1-1110000000000000000000000000000-222-211-1-1-1-1110000000000
χ5344-4-44-4-4400001-2-1-11-2221-2-12-121-23i−3i3i−3i3i−3i3i−3i000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000000000000000000000
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χ5744-4-44-4-44000044-4-444-4-444-4-4-4-44400000000000000000000000000000000000000000000000000000000000000
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χ764-4-444i−4i4i−4i−4i4i-441-2-11-122-2i−2i−i2ii−2i−i2i−i−iii-1-1112i−2i2-200000000−333−3i3−i3−i3i3i3−i3−i3i3−333−300000000000000000000000000
χ774-4-444i−4i4i−4i−4i4i-44-212-22-1-11−2ii2i−i−2ii2i−i2i2i−2i−2i22-2-2−ii-11000000000000000000000000000000003−3−i3i3i3−i3−330000000000
χ784-4-444i−4i4i−4i−4i4i-44-212-22-1-11−2ii2i−i−2ii2i−i2i2i−2i−2i22-2-2−ii-1100000000000000000000000000000000−33i3−i3−i3i33−30000000000
χ794-4-44−4i4i−4i4i4i−4i-441-2-11-122-2−i2ii−2i−i2ii−2iii−i−i-1-111−2i2i2-2000000003−3−33i3−i3−i3i3i3−i3−i3i33−3−3300000000000000000000000000
χ804-4-44−4i4i−4i4i4i−4i-441-2-11-122-2−i2ii−2i−i2ii−2iii−i−i-1-111−2i2i2-200000000−333−3−i3i3i3−i3−i3i3i3−i3−333−300000000000000000000000000
χ814-4-44−4i4i−4i4i4i−4i-44-212-22-1-112i−i−2ii2i−i−2ii−2i−2i2i2i22-2-2i−i-11000000000000000000000000000000003−3i3−i3−i3i3−330000000000
χ824-4-44−4i4i−4i4i4i−4i-44-212-22-1-112i−i−2ii2i−i−2ii−2i−2i2i2i22-2-2i−i-1100000000000000000000000000000000−33−i3i3i3−i33−30000000000
χ834-4-44−4i4i−4i4i−4i4i4-41-2-11-122-2−i2ii−2i−i2ii−2i−i−iii11-1-12i−2i-2200000000−i3i3i3−i33−3−33−333−3i3−i3−i3i300000000000000000000000000
χ844-4-44−4i4i−4i4i−4i4i4-41-2-11-122-2−i2ii−2i−i2ii−2i−i−iii11-1-12i−2i-2200000000i3−i3−i3i3−333−33−3−33−i3i3i3−i300000000000000000000000000
χ854-4-44−4i4i−4i4i−4i4i4-4-212-22-1-112i−i−2ii2i−i−2ii2i2i−2i−2i-2-222−ii1-1000000000000000000000000000000003−3i3−i3i3−i33−30000000000
χ864-4-44−4i4i−4i4i−4i4i4-4-212-22-1-112i−i−2ii2i−i−2ii2i2i−2i−2i-2-222−ii1-100000000000000000000000000000000−33−i3i3−i3i3−330000000000
χ8788-8-88-8-880000-4244-42-2-2-424-24-2-4200000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-888-80000-4244-42-2-24-2-42-424-200000000000000000000000000000000000000000000000000000000000000
χ898-88-88i8i−8i−8i0000-42-444-22-2−4i2i−4i2i4i−2i4i−2i00000000000000000000000000000000000000000000000000000000000000
χ908-88-8−8i−8i8i8i0000-42-444-22-24i−2i4i−2i−4i2i−4i2i00000000000000000000000000000000000000000000000000000000000000

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