Finite Group Databasebeta

← Group #11776932

Character table — Group #11776932

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222444444444444444488888888181818181818181818181818181818181818181818181818242424242424242424242424242424242424242424242424
order1222444422443366666612121212121212126666121212124444444488888888888888888888888824242424242424242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ511111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ711111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii
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χ2422-2-222-2-2000022-2-2-2-2222222-2-2-2-20000000000−2i2i−2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ2522-2-2-2-222000022-2-2-2-222-2-2-2-2222200000000002i−2i−2i2i0022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ2622-2-2-2-222000022-2-2-2-222-2-2-2-2222200000000002i−2i−2i2i00−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
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χ2822-2-2-2-222000022-2-2-2-222-2-2-2-222220000000000−2i2i2i−2i00−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
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χ322-22-22i−2i2i−2i00002222-2-2-2-22i2i−2i−2i2i2i−2i−2i00000000−2i2i0000-22−2i2i−2i2i-22-2200000000000000000000000000000000
χ332-22-2−2i2i−2i2i00002222-2-2-2-2−2i−2i2i2i−2i−2i2i2i000000002i−2i0000-222i−2i2i−2i-22-2200000000000000000000000000000000
χ342-22-2−2i2i−2i2i00002222-2-2-2-2−2i−2i2i2i−2i−2i2i2i000000002i−2i0000-22−2i2i−2i2i2-22-200000000000000000000000000000000
χ352-22-2−2i2i−2i2i00002222-2-2-2-2−2i−2i2i2i−2i−2i2i2i00000000−2i2i00002-2000000002-22-2−2i2i−2i2i000000000000000000000000
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χ382-2-222i−2i−2i2i2-22i−2i22-2-222-2-22i2i−2i−2i−2i−2i2i2i22-2-22i2i−2i−2i00000000i2−i2−i2i22−2−22i2−i2−i2i2−222−2000000000000000000000000
χ392-2-222i−2i−2i2i-22−2i2i22-2-222-2-22i2i−2i−2i−2i−2i2i2i-2-222−2i−2i2i2i00000000−i2i2i2−i2−222−2i2−i2−i2i2−222−2000000000000000000000000
χ402-2-222i−2i−2i2i-22−2i2i22-2-222-2-22i2i−2i−2i−2i−2i2i2i-2-222−2i−2i2i2i00000000i2−i2−i2i22−2−22−i2i2i2−i22−2−22000000000000000000000000
χ412-2-22−2i2i2i−2i2-2−2i2i22-2-222-2-2−2i−2i2i2i2i2i−2i−2i22-2-2−2i−2i2i2i00000000−i2i2i2−i22−2−22−i2i2i2−i2−222−2000000000000000000000000
χ422-2-22−2i2i2i−2i2-2−2i2i22-2-222-2-2−2i−2i2i2i2i2i−2i−2i22-2-2−2i−2i2i2i00000000i2−i2−i2i2−222−2i2−i2−i2i22−2−22000000000000000000000000
χ432-2-22−2i2i2i−2i-222i−2i22-2-222-2-2−2i−2i2i2i2i2i−2i−2i-2-2222i2i−2i−2i00000000−i2i2i2−i22−2−22i2−i2−i2i22−2−22000000000000000000000000
χ442-2-22−2i2i2i−2i-222i−2i22-2-222-2-2−2i−2i2i2i2i2i−2i−2i-2-2222i2i−2i−2i00000000i2−i2−i2i2−222−2−i2i2i2−i2−222−2000000000000000000000000
χ454444444444441-21-21-21-21-21-21-21-21-21-21-21-20000000000000000000000000000222200000000-1-1-1-1-1-1-1-1
χ464444444444441-21-21-21-21-21-21-21-21-21-21-21-20000000000000000000000000000-2-2-2-20000000011111111
χ47444444444444-21-21-21-21-21-21-21-21-21-21-21-2100000000000000000000000022220000-1-1-1-1-1-1-1-100000000
χ48444444444444-21-21-21-21-21-21-21-21-21-21-21-21000000000000000000000000-2-2-2-200001111111100000000
χ4944444444-4-4-4-41-21-21-21-21-21-21-21-2-12-12-12-12000000000000000000000000000022-2-200000000-1-1-1-11111
χ5044444444-4-4-4-41-21-21-21-21-21-21-21-2-12-12-12-120000000000000000000000000000-2-222000000001111-1-1-1-1
χ5144444444-4-4-4-4-21-21-21-21-21-21-21-212-12-12-12-100000000000000000000000022-2-20000-1-1-1-1111100000000
χ5244444444-4-4-4-4-21-21-21-21-21-21-21-212-12-12-12-1000000000000000000000000-2-22200001111-1-1-1-100000000
χ534444-4-4-4-444-4-41-21-21-21-2-12-12-12-121-21-2-12-1200000000000000000000000000002i−2i2i−2i00000000−i−iii−i−iii
χ544444-4-4-4-444-4-41-21-21-21-2-12-12-12-121-21-2-12-120000000000000000000000000000−2i2i−2i2i00000000ii−i−iii−i−i
χ554444-4-4-4-444-4-4-21-21-21-212-12-12-12-1-21-212-12-10000000000000000000000002i−2i2i−2i0000−i−iii−i−iii00000000
χ564444-4-4-4-444-4-4-21-21-21-212-12-12-12-1-21-212-12-1000000000000000000000000−2i2i−2i2i0000ii−i−iii−i−i00000000
χ574444-4-4-4-4-4-4441-21-21-21-2-12-12-12-12-12-121-21-200000000000000000000000000002i−2i−2i2i00000000−i−iiiii−i−i
χ584444-4-4-4-4-4-4441-21-21-21-2-12-12-12-12-12-121-21-20000000000000000000000000000−2i2i2i−2i00000000ii−i−i−i−iii
χ594444-4-4-4-4-4-444-21-21-21-212-12-12-12-12-12-1-21-210000000000000000000000002i−2i−2i2i0000−i−iiiii−i−i00000000
χ604444-4-4-4-4-4-444-21-21-21-212-12-12-12-12-12-1-21-21000000000000000000000000−2i2i2i−2i0000ii−i−i−i−iii00000000
χ614-4-444i−4i−4i4i4-44i−4i1-2-121-2-12i−2i−i2i−i2ii−2i1-2-12i−2i−i2i0000000000000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ624-4-444i−4i−4i4i4-44i−4i1-2-121-2-12i−2i−i2i−i2ii−2i1-2-12i−2i−i2i0000000000000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ634-4-444i−4i−4i4i4-44i−4i-212-1-212-1−2ii2i−i2i−i−2ii-212-1−2ii2i−i00000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ644-4-444i−4i−4i4i4-44i−4i-212-1-212-1−2ii2i−i2i−i−2ii-212-1−2ii2i−i00000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ654-4-444i−4i−4i4i-44−4i4i1-2-121-2-12i−2i−i2i−i2ii−2i-121-2−i2ii−2i0000000000000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ664-4-444i−4i−4i4i-44−4i4i1-2-121-2-12i−2i−i2i−i2ii−2i-121-2−i2ii−2i0000000000000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ674-4-444i−4i−4i4i-44−4i4i-212-1-212-1−2ii2i−i2i−i−2ii2-1-212i−i−2ii00000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ684-4-444i−4i−4i4i-44−4i4i-212-1-212-1−2ii2i−i2i−i−2ii2-1-212i−i−2ii00000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ694-4-44−4i4i4i−4i4-4−4i4i1-2-121-2-12−i2ii−2ii−2i−i2i1-2-12−i2ii−2i0000000000000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13
χ704-4-44−4i4i4i−4i4-4−4i4i1-2-121-2-12−i2ii−2ii−2i−i2i1-2-12−i2ii−2i0000000000000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
χ714-4-44−4i4i4i−4i4-4−4i4i-212-1-212-12i−i−2ii−2ii2i−i-212-12i−i−2ii00000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ724-4-44−4i4i4i−4i4-4−4i4i-212-1-212-12i−i−2ii−2ii2i−i-212-12i−i−2ii00000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ734-4-44−4i4i4i−4i-444i−4i1-2-121-2-12−i2ii−2ii−2i−i2i-121-2i−2i−i2i0000000000000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
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χ754-4-44−4i4i4i−4i-444i−4i-212-1-212-12i−i−2ii−2ii2i−i2-1-21−2ii2i−i00000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ764-4-44−4i4i4i−4i-444i−4i-212-1-212-12i−i−2ii−2ii2i−i2-1-21−2ii2i−i00000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ7788-8-888-8-800002-4-24-242-42-42-4-24-2400000000000000000000000000000000000000000000000000000000
χ7888-8-888-8-80000-424-24-2-42-42-424-24-200000000000000000000000000000000000000000000000000000000
χ7988-8-8-8-88800002-4-24-242-4-24-242-42-400000000000000000000000000000000000000000000000000000000
χ8088-8-8-8-8880000-424-24-2-424-24-2-42-4200000000000000000000000000000000000000000000000000000000
χ818-88-88i−8i8i−8i00002-42-4-24-242i−4i−2i4i2i−4i−2i4i00000000000000000000000000000000000000000000000000000000
χ828-88-88i−8i8i−8i0000-42-424-24-2−4i2i4i−2i−4i2i4i−2i00000000000000000000000000000000000000000000000000000000
χ838-88-8−8i8i−8i8i00002-42-4-24-24−2i4i2i−4i−2i4i2i−4i00000000000000000000000000000000000000000000000000000000
χ848-88-8−8i8i−8i8i0000-42-424-24-24i−2i−4i2i4i−2i−4i2i00000000000000000000000000000000000000000000000000000000

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