Finite Group Databasebeta

← Group #10706821

Character table — Group #10706821

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444466666666888888888812121212121212121212121216161616161616161616161648484848
order12223444444666888888121212121212161616161616161624242424444488882424484848484848484824881616161616161616888824242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−ii−ii−i
χ101111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−ii−ii
χ111111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111i−ii−iii−i−iii−i−i−ii−ii
χ121111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111−ii−ii−i−iii−i−iiii−ii−i
χ131111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiii−i−ii
χ141111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−iii−i
χ151111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1i−i−iiii−i−i−i−iii−iii−i
χ161111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−iii−i−i−iiiii−i−ii−i−ii
χ1722222222222222-2-2-2-2-2-222222200000000-2-2-2-22222-2-2-2-2-2-20000000022-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-222222200000000-2-2-2-2-2-2-2-22222-2-200000000-2-222000000000000000000000000
χ192222222-2-2-2-2222-2-2-2-22222-2-2-2-200000000-2-2-2-22222-2-2-2-22200000000-2-222000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-22222-2-2-2-200000000-2-2-2-2-2-2-2-22222220000000022-2-2000000000000000000000000
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χ2222222-2-222-2-2222000000-2-222-2-2−i2−i2i2i2−i2−i2i2i20000-2-222000000−i2−i2i2i2−i2−i2i2i2-2200i2i2−i2−i2i2i2−i2−i20000000000000000
χ2322222-2-222-2-2222000000-2-222-2-2i2i2−i2−i2i2i2−i2−i2000022-2-2000000i2i2−i2−i2i2i2−i2−i22-200i2i2−i2−i2i2i2−i2−i20000000000000000
χ2422222-2-222-2-2222000000-2-222-2-2i2i2−i2−i2i2i2−i2−i20000-2-222000000i2i2−i2−i2i2i2−i2−i2-2200−i2−i2i2i2−i2−i2i2i20000000000000000
χ2522222-2-2-2-222222000000-2-2-2-222−i2−i2i2i2i2i2−i2−i2000022-2-2000000−i2−i2i2i2i2i2−i2−i2-2200−i2−i2i2i2i2i2−i2−i20000000000000000
χ2622222-2-2-2-222222000000-2-2-2-222−i2−i2i2i2i2i2−i2−i20000-2-222000000−i2−i2i2i2i2i2−i2−i22-200i2i2−i2−i2−i2−i2i2i20000000000000000
χ2722222-2-2-2-222222000000-2-2-2-222i2i2−i2−i2−i2−i2i2i2000022-2-2000000i2i2−i2−i2−i2−i2i2i2-2200i2i2−i2−i2−i2−i2i2i20000000000000000
χ2822222-2-2-2-222222000000-2-2-2-222i2i2−i2−i2−i2−i2i2i20000-2-222000000i2i2−i2−i2−i2−i2i2i22-200−i2−i2i2i2i2i2−i2−i20000000000000000
χ292222-1222222-1-1-1222222-1-1-1-1-1-122222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-10000
χ302222-1222222-1-1-1222222-1-1-1-1-1-122222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2111111110000
χ312222-1222222-1-1-1222222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-1-11111111100000000000022-2-2-1-1-1-111110000
χ322222-1222222-1-1-1222222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-1-111111111000000000000-2-2221111-1-1-1-10000
χ332222-122-2-2-2-2-1-1-12222-2-2-1-111112222-2-2-2-2-1-1-1-10000000011-1-1-1-111110000000000002i−2i2i−2i−i−iii−i−iii0000
χ342222-122-2-2-2-2-1-1-12222-2-2-1-111112222-2-2-2-2-1-1-1-10000000011-1-1-1-11111000000000000−2i2i−2i2iii−i−iii−i−i0000
χ352222-122-2-2-2-2-1-1-12222-2-2-1-11111-2-2-2-22222-1-1-1-100000000111111-1-1-1-10000000000002i−2i−2i2i−i−iiiii−i−i0000
χ362222-122-2-2-2-2-1-1-12222-2-2-1-11111-2-2-2-22222-1-1-1-100000000111111-1-1-1-1000000000000−2i2i2i−2iii−i−i−i−iii0000
χ3722-2-222-22i−2i2i−2i2-2-20000002-22i−2i2i−2i2−22−2−i2i2−i2i20000000022-2-2002−22−2−i2i2−i2i2002i−2i2−22−2−i2i2−i2i20000000000000000
χ3822-2-222-22i−2i2i−2i2-2-20000002-22i−2i2i−2i2−22−2−i2i2−i2i200000000-2-222002−22−2−i2i2−i2i200−2i2i−22−22i2−i2i2−i20000000000000000
χ3922-2-222-22i−2i2i−2i2-2-20000002-22i−2i2i−2i−22−22i2−i2i2−i20000000022-2-200−22−22i2−i2i2−i2002i−2i−22−22i2−i2i2−i20000000000000000
χ4022-2-222-22i−2i2i−2i2-2-20000002-22i−2i2i−2i−22−22i2−i2i2−i200000000-2-22200−22−22i2−i2i2−i200−2i2i2−22−2−i2i2−i2i20000000000000000
χ4122-2-222-2−2i2i−2i2i2-2-20000002-2−2i2i−2i2i2−22−2i2−i2i2−i20000000022-2-2002−22−2i2−i2i2−i200−2i2i2−22−2i2−i2i2−i20000000000000000
χ4222-2-222-2−2i2i−2i2i2-2-20000002-2−2i2i−2i2i2−22−2i2−i2i2−i200000000-2-222002−22−2i2−i2i2−i2002i−2i−22−22−i2i2−i2i20000000000000000
χ4322-2-222-2−2i2i−2i2i2-2-20000002-2−2i2i−2i2i−22−22−i2i2−i2i20000000022-2-200−22−22−i2i2−i2i200−2i2i−22−22−i2i2−i2i20000000000000000
χ4422-2-222-2−2i2i−2i2i2-2-20000002-2−2i2i−2i2i−22−22−i2i2−i2i200000000-2-22200−22−22−i2i2−i2i2002i−2i2−22−2i2−i2i2−i20000000000000000
χ4522-2-22-222i−2i−2i2i2-2-222-2-22i−2i-222i−2i−2i2i0000000022-2-2000000002i−2i0000000000002i−2i−2i2i2-2-220000000000000000
χ4622-2-22-222i−2i−2i2i2-2-222-2-22i−2i-222i−2i−2i2i0000000022-2-2000000002i−2i000000000000−2i2i2i−2i-222-20000000000000000
χ4722-2-22-222i−2i−2i2i2-2-2-2-222−2i2i-222i−2i−2i2i2i−2i−2i2i2-2-22-2-22200000000−2i2i2i−2i−2i2i2-2-220000000000000000000000000000
χ4822-2-22-222i−2i−2i2i2-2-2-2-222−2i2i-222i−2i−2i2i−2i2i2i−2i-222-2-2-22200000000−2i2i−2i2i2i−2i-222-20000000000000000000000000000
χ4922-2-22-22−2i2i2i−2i2-2-222-2-2−2i2i-22−2i2i2i−2i0000000022-2-200000000−2i2i0000000000002i−2i−2i2i-222-20000000000000000
χ5022-2-22-22−2i2i2i−2i2-2-222-2-2−2i2i-22−2i2i2i−2i0000000022-2-200000000−2i2i000000000000−2i2i2i−2i2-2-220000000000000000
χ5122-2-22-22−2i2i2i−2i2-2-2-2-2222i−2i-22−2i2i2i−2i2i−2i−2i2i-222-2-2-222000000002i−2i2i−2i−2i2i-222-20000000000000000000000000000
χ5222-2-22-22−2i2i2i−2i2-2-2-2-2222i−2i-22−2i2i2i−2i−2i2i2i−2i2-2-22-2-222000000002i−2i−2i2i2i−2i2-2-220000000000000000000000000000
χ5322-2-2-1-222i−2i−2i2i-111-2-222−2i2i1-1−iii−i2i−2i−2i2i2-2-2211-1-100000000i−i−iii−i-111-10000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ5422-2-2-1-222i−2i−2i2i-111-2-222−2i2i1-1−iii−i2i−2i−2i2i2-2-2211-1-100000000i−i−iii−i-111-10000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ5522-2-2-1-222i−2i−2i2i-111-2-222−2i2i1-1−iii−i−2i2i2i−2i-222-211-1-100000000i−ii−i−ii1-1-110000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ5622-2-2-1-222i−2i−2i2i-111-2-222−2i2i1-1−iii−i−2i2i2i−2i-222-211-1-100000000i−ii−i−ii1-1-110000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ5722-2-2-1-22−2i2i2i−2i-111-2-2222i−2i1-1i−i−ii2i−2i−2i2i-222-211-1-100000000−ii−iii−i1-1-110000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ5822-2-2-1-22−2i2i2i−2i-111-2-2222i−2i1-1i−i−ii2i−2i−2i2i-222-211-1-100000000−ii−iii−i1-1-110000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ5922-2-2-1-22−2i2i2i−2i-111-2-2222i−2i1-1i−i−ii−2i2i2i−2i2-2-2211-1-100000000−iii−i−ii-111-10000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ6022-2-2-1-22−2i2i2i−2i-111-2-2222i−2i1-1i−i−ii−2i2i2i−2i2-2-2211-1-100000000−iii−i−ii-111-10000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ614444-2444444-2-2-2-4-4-4-4-4-4-2-2-2-2-2-20000000022220000000022000000000000000000000000000000000000
χ624444-244-4-4-4-4-2-2-2-4-4-4-444-2-2222200000000222200000000-2-2000000000000000000000000000000000000
χ634444-2-4-444-4-4-2-2-200000022-2-222−2i2−2i22i22i2−2i2−2i22i22i200000000000000i2i2−i2−i2i2i2−i2−i20000000000000000000000000000
χ644444-2-4-444-4-4-2-2-200000022-2-2222i22i2−2i2−2i22i22i2−2i2−2i200000000000000−i2−i2i2i2−i2−i2i2i20000000000000000000000000000
χ654444-2-4-4-4-444-2-2-20000002222-2-2−2i2−2i22i22i22i22i2−2i2−2i200000000000000i2i2−i2−i2−i2−i2i2i20000000000000000000000000000
χ664444-2-4-4-4-444-2-2-20000002222-2-22i22i2−2i2−2i2−2i2−2i22i22i200000000000000−i2−i2i2i2i2i2−i2−i20000000000000000000000000000
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χ818-88-8-40000004-44−4i24i2−4i24i200000000000000002i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ828-88-8-40000004-444i2−4i24i2−4i20000000000000000−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ838-8-88-400000044-4−4i24i24i2−4i200000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ848-8-88-400000044-44i2−4i2−4i24i20000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000000000

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