Finite Group Databasebeta

← Group #10694728

Character table — Group #10694728

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12222234444444466688888888121212124466888812121212121212121212242424242424242424242424242424248888888888888888888824242424242424242244
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
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-11
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-11-11
χ8111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111-11-1
χ9111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i11-1-1
χ10111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-1-111
χ11111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i-1-111
χ12111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii11-1-1
χ13111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii1-1-11
χ14111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-111-1
χ15111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-111-1
χ16111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i1-1-11
χ172222222-2-22222-2-2222000000002222-2-2220000-2-222-2-2-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ182222222-2-22222-2-2222000000002222-2-2220000-2-222-2-2-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ192222222-2-2-2-2-2-22222200000000-2-2-2-22-2220000-2-2-2-22222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ202222222-2-2-2-2-2-22222200000000-2-2-2-22-2220000-2-2-2-22222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ21222222-122222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ22222222-122222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ23222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ24222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ25222222-122-2-2-2-2-2-2-1-1-12222-2-2-2-21111-22-1-122-2-2-1-1111111-1-1-1-1-1-1-1-1-1-11111111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ26222222-122-2-2-2-2-2-2-1-1-12222-2-2-2-21111-22-1-122-2-2-1-1111111-1-1-1-1-1-1-1-1-1-1111111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ27222222-122-2-2-2-2-2-2-1-1-1-2-2-2-222221111-22-1-1-2-222-1-1111111-1-111111111-1-1-1-1-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ28222222-122-2-2-2-2-2-2-1-1-1-2-2-2-222221111-22-1-1-2-222-1-1111111-1-111111111-1-1-1-1-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ292222-2-222222-2-2-2-22222222-2-2-2-222222-2-2-2-2-222-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ302222-2-222222-2-2-2-2222-2-2-2-2222222222-2-2-222-2-2-2-2-2-222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ312222-2-2222-2-2222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ322222-2-2222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-22222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ332222-2-22-2-222-2-222222000000002222-22-2-2000022-2-2-2-222-2-2000000000000000022-2-222-2-2000000000000000000000000
χ342222-2-22-2-222-2-222222000000002222-22-2-2000022-2-2-2-222-2-20000000000000000-2-222-2-222000000000000000000000000
χ352222-2-22-2-2-2-222-2-222200000000-2-2-2-222-2-20000222222-2-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ362222-2-22-2-2-2-222-2-222200000000-2-2-2-222-2-20000222222-2-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ372222-2-2-12222-2-2-2-2-1-1-12222-2-2-2-2-1-1-1-12-211-2-2221111-1-111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ382222-2-2-12222-2-2-2-2-1-1-12222-2-2-2-2-1-1-1-12-211-2-2221111-1-111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ392222-2-2-12222-2-2-2-2-1-1-1-2-2-2-22222-1-1-1-12-21122-2-21111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ402222-2-2-12222-2-2-2-2-1-1-1-2-2-2-22222-1-1-1-12-21122-2-21111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ412222-2-2-122-2-22222-1-1-1222222221111-2-211-2-2-2-211-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1000000000000000000003−3−333−3−330000
χ422222-2-2-122-2-22222-1-1-1222222221111-2-211-2-2-2-211-1-111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000−333−3−333−30000
χ432222-2-2-122-2-22222-1-1-1-2-2-2-2-2-2-2-21111-2-211222211-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000000000003−3−33−333−30000
χ442222-2-2-122-2-22222-1-1-1-2-2-2-2-2-2-2-21111-2-211222211-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−333−33−3−330000
χ4522-2-22-22002i−2i2i−2i002-2-222−2−2−i2−i2i2i22i2i−2i−2i002-22−2−i2i2002i−2i00000022−2−222−2−2−i2−i2i2i2−i2−i2i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ4622-2-22-22002i−2i2i−2i002-2-222−2−2−i2−i2i2i22i2i−2i−2i002-22−2−i2i2002i−2i00000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ4722-2-22-22002i−2i2i−2i002-2-2−2−222i2i2−i2−i22i2i−2i−2i002-2−22i2−i2002i−2i000000−2−222−2−222i2i2−i2−i2i2i2−i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ4822-2-22-22002i−2i2i−2i002-2-2−2−222i2i2−i2−i22i2i−2i−2i002-2−22i2−i2002i−2i000000−2−222−2−222i2i2−i2−i2i2i2−i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ4922-2-22-2200−2i2i−2i2i002-2-222−2−2i2i2−i2−i2−2i−2i2i2i002-22−2i2−i200−2i2i00000022−2−222−2−2i2i2−i2−i2i2i2−i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ5022-2-22-2200−2i2i−2i2i002-2-222−2−2i2i2−i2−i2−2i−2i2i2i002-22−2i2−i200−2i2i00000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ5122-2-22-2200−2i2i−2i2i002-2-2−2−222−i2−i2i2i2−2i−2i2i2i002-2−22−i2i200−2i2i000000−2−222−2−222−i2−i2i2i2−i2−i2i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ5222-2-22-2200−2i2i−2i2i002-2-2−2−222−i2−i2i2i2−2i−2i2i2i002-2−22−i2i200−2i2i000000−2−222−2−222−i2−i2i2i2−i2−i2i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ5322-2-2-222002i−2i−2i2i002-2-222−2−2i2i2−i2−i22i2i−2i−2i00-22−22−i2i200−2i2i00000022−2−2−2−222−i2−i2i2i2i2i2−i2−i21+i−1−i−1−i1+i1−i−1+i−1+i1−i2ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ5422-2-2-222002i−2i−2i2i002-2-222−2−2i2i2−i2−i22i2i−2i−2i00-22−22−i2i200−2i2i00000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ5522-2-2-222002i−2i−2i2i002-2-2−2−222−i2−i2i2i22i2i−2i−2i00-222−2i2−i200−2i2i000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i21+i−1−i−1−i1+i1−i−1+i−1+i1−i−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ5622-2-2-222002i−2i−2i2i002-2-2−2−222−i2−i2i2i22i2i−2i−2i00-222−2i2−i200−2i2i000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i2ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ5722-2-2-22200−2i2i2i−2i002-2-222−2−2−i2−i2i2i2−2i−2i2i2i00-22−22i2−i2002i−2i00000022−2−2−2−222i2i2−i2−i2−i2−i2i2i21−i−1+i−1+i1−i1+i−1−i−1−i1+i−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ5822-2-2-22200−2i2i2i−2i002-2-222−2−2−i2−i2i2i2−2i−2i2i2i00-22−22i2−i2002i−2i00000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i2ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ5922-2-2-22200−2i2i2i−2i002-2-2−2−222i2i2−i2−i2−2i−2i2i2i00-222−2−i2i2002i−2i000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i21−i−1+i−1+i1−i1+i−1−i−1−i1+i2ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ6022-2-2-22200−2i2i2i−2i002-2-2−2−222i2i2−i2−i2−2i−2i2i2i00-222−2−i2i2002i−2i000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ61444444-2-4-44444-4-4-2-2-200000000-2-2-2-2-4-4-2-2000022-2-2222222000000000000000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-444-2-2-20000000022224-4-2-200002222-2-2-2-222000000000000000000000000000000000000000000000000
χ634444-4-4-2-4-444-4-444-2-2-200000000-2-2-2-2-44220000-2-22222-2-222000000000000000000000000000000000000000000000000
χ644444-4-4-2-4-4-4-444-4-4-2-2-200000000222244220000-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ6544-4-44-4-2004i−4i4i−4i00-2222222−22−22−2i2−2i22i22i2−2i−2i2i2i00-2222−22−2i22i200−2i2i000000−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ6644-4-44-4-2004i−4i4i−4i00-222−22−2222222i22i2−2i2−2i2−2i−2i2i2i00-22−22222i2−2i200−2i2i00000022−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ6744-4-44-4-200−4i4i−4i4i00-2222222−22−222i22i2−2i2−2i22i2i−2i−2i00-2222−222i2−2i2002i−2i000000−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ6844-4-44-4-200−4i4i−4i4i00-222−22−222222−2i2−2i22i22i22i2i−2i−2i00-22−2222−2i22i2002i−2i00000022−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ6944-4-4-44-2004i−4i−4i4i00-2222222−22−222i22i2−2i2−2i2−2i−2i2i2i002-2−2222−2i22i2002i−2i000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ7044-4-4-44-2004i−4i−4i4i00-222−22−222222−2i2−2i22i22i2−2i−2i2i2i002-222−222i2−2i2002i−2i00000022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ7144-4-4-44-200−4i4i4i−4i00-2222222−22−22−2i2−2i22i22i22i2i−2i−2i002-2−22222i2−2i200−2i2i000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ7244-4-4-44-200−4i4i4i−4i00-222−22−2222222i22i2−2i2−2i22i2i−2i−2i002-222−22−2i22i200−2i2i00000022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ734-44-40040000004i−4i-44-422−2222−22−2i22i2−2i22i20000000000000000004i−4i0022−2222−2200000000−2i22i2−2i22i200000000000000000000000000000000
χ744-44-40040000004i−4i-44-4−2222−22222i2−2i22i2−2i20000000000000000004i−4i00−2222−2222000000002i2−2i22i2−2i200000000000000000000000000000000
χ754-44-4004000000−4i4i-44-422−2222−222i2−2i22i2−2i2000000000000000000−4i4i0022−2222−22000000002i2−2i22i2−2i200000000000000000000000000000000
χ764-44-4004000000−4i4i-44-4−2222−2222−2i22i2−2i22i2000000000000000000−4i4i00−2222−222200000000−2i22i2−2i22i200000000000000000000000000000000
χ774-44-400-20000004i−4i2-2222−2222−22−2i22i2−2i22i2−2i32i3−2i32i30000000023−230000−2i2i00−22−226−66−6i6−i6i6−i6i2−i2i2−i200000000000000000000000000000000
χ784-44-400-20000004i−4i2-2222−2222−22−2i22i2−2i22i22i3−2i32i3−2i300000000−23230000−2i2i00−22−22−66−66−i6i6−i6i6i2−i2i2−i200000000000000000000000000000000
χ794-44-400-20000004i−4i2-22−2222−22222i2−2i22i2−2i2−2i32i3−2i32i30000000023−230000−2i2i002−22−2−66−66−i6i6−i6i6−i2i2−i2i200000000000000000000000000000000
χ804-44-400-20000004i−4i2-22−2222−22222i2−2i22i2−2i22i3−2i32i3−2i300000000−23230000−2i2i002−22−26−66−6i6−i6i6−i6−i2i2−i2i200000000000000000000000000000000
χ814-44-400-2000000−4i4i2-2222−2222−222i2−2i22i2−2i2−2i32i3−2i32i300000000−232300002i−2i00−22−22−66−66i6−i6i6−i6−i2i2−i2i200000000000000000000000000000000
χ824-44-400-2000000−4i4i2-2222−2222−222i2−2i22i2−2i22i3−2i32i3−2i30000000023−2300002i−2i00−22−226−66−6−i6i6−i6i6−i2i2−i2i200000000000000000000000000000000
χ834-44-400-2000000−4i4i2-22−2222−2222−2i22i2−2i22i2−2i32i3−2i32i300000000−232300002i−2i002−22−26−66−6−i6i6−i6i6i2−i2i2−i200000000000000000000000000000000
χ844-44-400-2000000−4i4i2-22−2222−2222−2i22i2−2i22i22i3−2i32i3−2i30000000023−2300002i−2i002−22−2−66−66i6−i6i6−i6i2−i2i2−i200000000000000000000000000000000
χ854-4-440044-4000000-4-4400004-4-44000000000000000000004-40000000000004-4-4400000000000000000000000000000000
χ864-4-440044-4000000-4-440000-444-4000000000000000000004-4000000000000-444-400000000000000000000000000000000
χ874-4-44004-44000000-4-444-4-44000000000000000000000000-444-4-4400000000000000000000000000000000000000000000
χ884-4-44004-44000000-4-44-444-4000000000000000000000000-44-444-400000000000000000000000000000000000000000000
χ894-4-4400-24-400000022-200004-4-4423−23−232300000000000023−2300-220000−232323−230000-222-200000000000000000000000000000000
χ904-4-4400-24-400000022-200004-4-44−232323−23000000000000−232300-22000023−23−23230000-222-200000000000000000000000000000000
χ914-4-4400-24-400000022-20000-444-423−23−232300000000000023−2300-22000023−23−232300002-2-2200000000000000000000000000000000
χ924-4-4400-24-400000022-20000-444-4−232323−23000000000000−232300-220000−232323−2300002-2-2200000000000000000000000000000000
χ934-4-4400-2-4400000022-24-4-44000023−23−2323000000000000−2323002-2-222-2000023−23−2323000000000000000000000000000000000000
χ944-4-4400-2-4400000022-24-4-440000−232323−2300000000000023−23002-2-222-20000−232323−23000000000000000000000000000000000000
χ954-4-4400-2-4400000022-2-444-4000023−23−2323000000000000−2323002-22-2-220000−232323−23000000000000000000000000000000000000
χ964-4-4400-2-4400000022-2-444-40000−232323−2300000000000023−23002-22-2-22000023−23−2323000000000000000000000000000000000000

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