Finite Group Databasebeta

← Group #10694898

Character table — Group #10694898

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order1222222234444446668888888812121212246666668888121212121212242424242424242424242424242424244444444488888888888824242424242424242244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11-1
χ6111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-11
χ7111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-11-11
χ8111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111-11-1
χ9111111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i11-1-1
χ10111111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-1-111
χ11111111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i-1-111
χ12111111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii11-1-1
χ13111111-1-1111-1-1-1-1111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii1-1-11
χ14111111-1-1111-1-1-1-1111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-111-1
χ15111111-1-1111-1-1-1-1111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-111-1
χ16111111-1-1111-1-1-1-1111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i1-1-11
χ17222222222-2-2-2-2-2-222200000000-2-2-2-22-22222220000-2-2-2-2-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ18222222222-2-2-2-2-2-222200000000-2-2-2-22-22222220000-2-2-2-2-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ1922222222-1222222-1-1-122222222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2022222222-1222222-1-1-122222222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2122222222-1222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ2222222222-1222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ23222222-2-22-2-22222222000000002222-2-222-2-2-2-20000-2-2-222-200000000000000000000000022-2-2-2-2220000000000000000
χ24222222-2-22-2-22222222000000002222-2-222-2-2-2-20000-2-2-222-2000000000000000000000000-2-22222-2-20000000000000000
χ25222222-2-2-122-2-2-2-2-1-1-12222-2-2-2-21111-22-1-1111122-2-2-1-1-111-1-1-1-1-1-1-1-1-11111111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ26222222-2-2-122-2-2-2-2-1-1-12222-2-2-2-21111-22-1-1111122-2-2-1-1-111-1-1-1-1-1-1-1-1-1111111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ27222222-2-2-122-2-2-2-2-1-1-1-2-2-2-222221111-22-1-11111-2-222-1-1-111-111111111-1-1-1-1-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ28222222-2-2-122-2-2-2-2-1-1-1-2-2-2-222221111-22-1-11111-2-222-1-1-111-111111111-1-1-1-1-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ292222-2-222222-2-22222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-22-2-22222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ302222-2-222222-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222222-2-2222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ312222-2-2222-2-222-2-2222000000002222-22-2-222-2-20000-222-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ322222-2-2222-2-222-2-2222000000002222-22-2-222-2-20000-222-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ332222-2-222-122-2-222-1-1-1222222221111-2-211-1-111-2-2-2-2-111-1-1-1-1-1-1-11111-1-1-1-11111000000000000000000003−33−33−33−30000
χ342222-2-222-122-2-222-1-1-1222222221111-2-211-1-111-2-2-2-2-111-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−33−33−33−330000
χ352222-2-222-122-2-222-1-1-1-2-2-2-2-2-2-2-21111-2-211-1-1112222-111-1-1-11111-1-1-1-11111-1-1-1-1000000000000000000003−33−3−33−330000
χ362222-2-222-122-2-222-1-1-1-2-2-2-2-2-2-2-21111-2-211-1-1112222-111-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000−33−333−33−30000
χ372222-2-2-2-222222-2-22222222-2-2-2-222222-2-2-2-2-222-2-2222-2-2-2-222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ382222-2-2-2-222222-2-2222-2-2-2-2222222222-2-2-2-2-22222-2-22-2-2-2-22-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ392222-2-2-2-22-2-2-2-22222200000000-2-2-2-222-2-2-2-2220000-22222-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ402222-2-2-2-22-2-2-2-22222200000000-2-2-2-222-2-2-2-2220000-22222-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ412222-2-2-2-2-12222-2-2-1-1-12222-2-2-2-2-1-1-1-12-21111-1-1-2-222-11111-1-1-1-1-111111111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ422222-2-2-2-2-12222-2-2-1-1-12222-2-2-2-2-1-1-1-12-21111-1-1-2-222-11111-1-1-1-1-111111111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ432222-2-2-2-2-12222-2-2-1-1-1-2-2-2-22222-1-1-1-12-21111-1-122-2-2-11111-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ442222-2-2-2-2-12222-2-2-1-1-1-2-2-2-22222-1-1-1-12-21111-1-122-2-2-11111-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ4522-2-22-2002002i−2i2i−2i2-2-222−2−2−i2−i2i2i22i2i−2i−2i002-200002−2−i2i20002i−2i022−2−222−2−2−i2−i2i2i2−i2−i2i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ4622-2-22-2002002i−2i2i−2i2-2-222−2−2−i2−i2i2i22i2i−2i−2i002-200002−2−i2i20002i−2i022−2−222−2−2−i2−i2i2i2−i2−i2i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ4722-2-22-2002002i−2i2i−2i2-2-2−2−222i2i2−i2−i22i2i−2i−2i002-20000−22i2−i20002i−2i0−2−222−2−222i2i2−i2−i2i2i2−i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ4822-2-22-2002002i−2i2i−2i2-2-2−2−222i2i2−i2−i22i2i−2i−2i002-20000−22i2−i20002i−2i0−2−222−2−222i2i2−i2−i2i2i2−i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ4922-2-22-200200−2i2i−2i2i2-2-222−2−2i2i2−i2−i2−2i−2i2i2i002-200002−2i2−i2000−2i2i022−2−222−2−2i2i2−i2−i2i2i2−i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ5022-2-22-200200−2i2i−2i2i2-2-222−2−2i2i2−i2−i2−2i−2i2i2i002-200002−2i2−i2000−2i2i022−2−222−2−2i2i2−i2−i2i2i2−i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ5122-2-22-200200−2i2i−2i2i2-2-2−2−222−i2−i2i2i2−2i−2i2i2i002-20000−22−i2i2000−2i2i0−2−222−2−222−i2−i2i2i2−i2−i2i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ5222-2-22-200200−2i2i−2i2i2-2-2−2−222−i2−i2i2i2−2i−2i2i2i002-20000−22−i2i2000−2i2i0−2−222−2−222−i2−i2i2i2−i2−i2i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ5322-2-2-22002002i−2i−2i2i2-2-222−2−2i2i2−i2−i22i2i−2i−2i00-220000−22−i2i2000−2i2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i21+i−1−i−1−i1+i1−i−1+i−1+i1−i2ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ5422-2-2-22002002i−2i−2i2i2-2-222−2−2i2i2−i2−i22i2i−2i−2i00-220000−22−i2i2000−2i2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ5522-2-2-22002002i−2i−2i2i2-2-2−2−222−i2−i2i2i22i2i−2i−2i00-2200002−2i2−i2000−2i2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i21+i−1−i−1−i1+i1−i−1+i−1+i1−i−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ5622-2-2-22002002i−2i−2i2i2-2-2−2−222−i2−i2i2i22i2i−2i−2i00-2200002−2i2−i2000−2i2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i2ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ5722-2-2-2200200−2i2i2i−2i2-2-222−2−2−i2−i2i2i2−2i−2i2i2i00-220000−22i2−i20002i−2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i21−i−1+i−1+i1−i1+i−1−i−1−i1+i−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ5822-2-2-2200200−2i2i2i−2i2-2-222−2−2−i2−i2i2i2−2i−2i2i2i00-220000−22i2−i20002i−2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i2ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ5922-2-2-2200200−2i2i2i−2i2-2-2−2−222i2i2−i2−i2−2i−2i2i2i00-2200002−2−i2i20002i−2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i21−i−1+i−1+i1−i1+i−1−i−1−i1+i2ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ6022-2-2-2200200−2i2i2i−2i2-2-2−2−222i2i2−i2−i2−2i−2i2i2i00-2200002−2−i2i20002i−2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ6144444444-2-4-4-4-4-4-4-2-2-20000000022224-4-2-2-2-2-2-20000222222000000000000000000000000000000000000000000000000
χ62444444-4-4-2-4-44444-2-2-200000000-2-2-2-2-4-4-2-222220000222-2-22000000000000000000000000000000000000000000000000
χ634444-4-444-2-4-444-4-4-2-2-200000000-2-2-2-2-4422-2-22200002-2-2222000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-2-4-4-4-444-2-2-2000000002222442222-2-200002-2-2-2-22000000000000000000000000000000000000000000000000
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χ6644-4-44-400-2004i−4i4i−4i-222−22−2222222i22i2−2i2−2i2−2i−2i2i2i00-220000−22222i2−2i2000−2i2i022−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ6744-4-44-400-200−4i4i−4i4i-2222222−22−222i22i2−2i2−2i22i2i−2i−2i00-22000022−222i2−2i20002i−2i0−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ6844-4-44-400-200−4i4i−4i4i-222−22−222222−2i2−2i22i22i22i2i−2i−2i00-220000−2222−2i22i20002i−2i022−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ6944-4-4-4400-2004i−4i−4i4i-2222222−22−222i22i2−2i2−2i2−2i−2i2i2i002-20000−2222−2i22i20002i−2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ7044-4-4-4400-2004i−4i−4i4i-222−22−222222−2i2−2i22i22i2−2i−2i2i2i002-2000022−222i2−2i20002i−2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ7144-4-4-4400-200−4i4i4i−4i-2222222−22−22−2i2−2i22i22i22i2i−2i−2i002-20000−22222i2−2i2000−2i2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ7244-4-4-4400-200−4i4i4i−4i-222−22−2222222i22i2−2i2−2i22i2i−2i−2i002-2000022−22−2i22i2000−2i2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
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χ744-44-4000044-40000-4-440000−4i4i−4i4i000000000000000040000-400000000−4i4i−4i4i000000000000000000000000000000000000
χ754-44-400004-440000-4-444-44-400000000000000000000-4000044-44-400000000000000000000000000000000000000000000
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χ824-44-40000-2-44000022-24-44-400002i3−2i32i3−2i3000000−2i32i3000020000-2-22-22000000002i3−2i32i3−2i300000000000000000000000000000000
χ834-44-40000-2-44000022-2-44-440000−2i32i3−2i32i30000002i3−2i3000020000-22-22-2000000002i3−2i32i3−2i300000000000000000000000000000000
χ844-44-40000-2-44000022-2-44-4400002i3−2i32i3−2i3000000−2i32i3000020000-22-22-200000000−2i32i3−2i32i300000000000000000000000000000000
χ854-4-44004-44000000-44-422−22−222222−22−2222000000004-400000000000022−22−2222000022−22−2222000000000000000000000000000000000000
χ864-4-44004-44000000-44-4−222222−22−222222−22000000004-4000000000000−222222−220000−222222−22000000000000000000000000000000000000
χ874-4-44004-4-20000002-2222−22−222222−22−222223−23−23230000-22000000023−23000−222−26−6−66−222−2−666−600000000000000000000000000000000
χ884-4-44004-4-20000002-2222−22−222222−22−2222−232323−230000-220000000−2323000−222−2−666−6−222−26−6−6600000000000000000000000000000000
χ894-4-44004-4-20000002-22−222222−22−222222−2223−23−23230000-22000000023−230002−2−22−666−62−2−226−6−6600000000000000000000000000000000
χ904-4-44004-4-20000002-22−222222−22−222222−22−232323−230000-220000000−23230002−2−226−6−662−2−22−666−600000000000000000000000000000000
χ914-4-4400-444000000-44-422−22−2222−222222−2200000000-4400000000000022−22−22220000−222222−22000000000000000000000000000000000000
χ924-4-4400-444000000-44-4−222222−2222−22−222200000000-44000000000000−222222−22000022−22−2222000000000000000000000000000000000000
χ934-4-4400-44-20000002-2222−22−2222−222222−2223−23−232300002-20000000−2323000−222−2−666−62−2−22−666−600000000000000000000000000000000
χ944-4-4400-44-20000002-2222−22−2222−222222−22−232323−2300002-2000000023−23000−222−26−6−662−2−226−6−6600000000000000000000000000000000
χ954-4-4400-44-20000002-22−222222−2222−22−222223−23−232300002-20000000−23230002−2−226−6−66−222−26−6−6600000000000000000000000000000000
χ964-4-4400-44-20000002-22−222222−2222−22−2222−232323−2300002-2000000023−230002−2−22−666−6−222−2−666−600000000000000000000000000000000

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