Finite Group Databasebeta

← Group #10694890

Character table — Group #10694890

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122222223444444666666688888888246666888812121212121212122424242424242424242424242424242444444444888888882444661212121212128888
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
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ9111111-1-1111-1-1-1-111111111111-1-1-1-1-11-1-1-1-111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-111-1-1i−ii−i
χ10111111-1-1111-1-1-1-111111111111-1-1-1-1-11-1-1-1-111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111-1-111−ii−ii
χ11111111-1-1111-1-1-1-111111111111-1-1-1-1-11-1-1-1-111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-111-1-1−ii−ii
χ12111111-1-1111-1-1-1-111111111111-1-1-1-1-11-1-1-1-111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111-1-111i−ii−i
χ13111111-1-1111-1-1-1-11111111-1-1-1-11111-11-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111i−i−ii
χ14111111-1-1111-1-1-1-11111111-1-1-1-11111-11-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−iii−i
χ15111111-1-1111-1-1-1-11111111-1-1-1-11111-11-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−iii−i
χ16111111-1-1111-1-1-1-11111111-1-1-1-11111-11-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1i−i−ii
χ17222222222-2-2-2-2-2-22222222000000002-222220000-2-2-2-2-2-2-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ18222222222-2-2-2-2-2-22222222000000002-222220000-2-2-2-2-2-2-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ1922222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2022222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2122222222-1222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ2222222222-1222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ23222222-2-22-2-22222222222200000000-2-2-2-2-2-20000-2-2-22222-200000000000000000000000022-2-2-2-2220000000000000000
χ24222222-2-22-2-22222222222200000000-2-2-2-2-2-20000-2-2-22222-2000000000000000000000000-2-22222-2-20000000000000000
χ25222222-2-2-122-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-22111122-2-2-1-1-11111-1-1-1-1-1-1-1-1-11111111100000000000000002-22-2-1-111-1-1110000
χ26222222-2-2-122-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-22111122-2-2-1-1-11111-1-1-1-1-1-1-1-1-1111111110000000000000000-22-2211-1-111-1-10000
χ27222222-2-2-122-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22222-221111-2-222-1-1-11111-111111111-1-1-1-1-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ28222222-2-2-122-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22222-221111-2-222-1-1-11111-111111111-1-1-1-1-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ292222-2-22222222-2-2-2-2-2-222222222222-2-222-2-2-2-2-2-22-2-222-2-222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ302222-2-22222222-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-222-2-222222-2-222-2-22-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ312222-2-2222-2-2-2-222-2-2-2-222200000000-2222-2-20000-222-2-222-2000000000000000022-2-222-2-2000000000000000000000000
χ322222-2-2222-2-2-2-222-2-2-2-222200000000-2222-2-20000-222-2-222-20000000000000000-2-222-2-222000000000000000000000000
χ332222-2-222-12222-2-21111-1-1-122222222-2-2-1-111-2-2-2-2-111-1-111-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ342222-2-222-12222-2-21111-1-1-122222222-2-2-1-111-2-2-2-2-111-1-111-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ352222-2-222-12222-2-21111-1-1-1-2-2-2-2-2-2-2-2-2-2-1-1112222-111-1-111-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ362222-2-222-12222-2-21111-1-1-1-2-2-2-2-2-2-2-2-2-2-1-1112222-111-1-111-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ372222-2-2-2-2222-2-222-2-2-2-22222222-2-2-2-22-2-2-222-2-2222-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ382222-2-2-2-2222-2-222-2-2-2-2222-2-2-2-222222-2-2-22222-2-22-2-2-2-2222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ392222-2-2-2-22-2-222-2-2-2-2-2-22220000000022-2-2220000-22222-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ402222-2-2-2-22-2-222-2-2-2-2-2-22220000000022-2-2220000-22222-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ412222-2-2-2-2-122-2-2221111-1-1-12222-2-2-2-22-211-1-1-2-222-11111-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ422222-2-2-2-2-122-2-2221111-1-1-12222-2-2-2-22-211-1-1-2-222-11111-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ432222-2-2-2-2-122-2-2221111-1-1-1-2-2-2-222222-211-1-122-2-2-11111-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ442222-2-2-2-2-122-2-2221111-1-1-1-2-2-2-222222-211-1-122-2-2-11111-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ4522-2-22-2002002i−2i2i−2i22-2-22-2-222−2−2−i2−i2i2i20000002−2−i2i20002i−2i2i−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−2i22-2-22-2-222−2−2−i2−i2i2i20000002−2−i2i20002i−2i2i−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−2i22-2-22-2-2−2−222i2i2−i2−i2000000−22i2−i20002i−2i2i−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−2i22-2-22-2-2−2−222i2i2−i2−i2000000−22i2−i20002i−2i2i−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−2i2i22-2-22-2-222−2−2i2i2−i2−i20000002−2i2−i2000−2i2i−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−2i2i22-2-22-2-222−2−2i2i2−i2−i20000002−2i2−i2000−2i2i−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−2i2i22-2-22-2-2−2−222−i2−i2i2i2000000−22−i2i2000−2i2i−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−2i2i22-2-22-2-2−2−222−i2−i2i2i2000000−22−i2i2000−2i2i−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−2i2i-2-2222-2-222−2−2−i2−i2i2i2000000−22i2−i20002i−2i−2i2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i21−i−1+i−1+i1−i1+i−1−i−1−i1+i−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ5422-2-2-22002002i−2i−2i2i-2-2222-2-222−2−2−i2−i2i2i2000000−22i2−i20002i−2i−2i2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i2ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ5522-2-2-22002002i−2i−2i2i-2-2222-2-2−2−222i2i2−i2−i20000002−2−i2i20002i−2i−2i2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i21−i−1+i−1+i1−i1+i−1−i−1−i1+i2ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ5622-2-2-22002002i−2i−2i2i-2-2222-2-2−2−222i2i2−i2−i20000002−2−i2i20002i−2i−2i2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ5722-2-2-2200200−2i2i2i−2i-2-2222-2-222−2−2i2i2−i2−i2000000−22−i2i2000−2i2i2i−2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i21+i−1−i−1−i1+i1−i−1+i−1+i1−i2ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ5822-2-2-2200200−2i2i2i−2i-2-2222-2-222−2−2i2i2−i2−i2000000−22−i2i2000−2i2i2i−2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ130000000000000000
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χ6022-2-2-2200200−2i2i2i−2i-2-2222-2-2−2−222−i2−i2i2i20000002−2i2−i2000−2i2i2i−2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i2ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ6144444444-2-4-4-4-4-4-4-2-2-2-2-2-2-2000000004-4-2-2-2-2000022222222000000000000000000000000000000000000000000000000
χ62444444-4-4-2-4-44444-2-2-2-2-2-2-200000000-4-422220000222-2-2-2-22000000000000000000000000000000000000000000000000
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χ7044-4-4-4400-2004i−4i−4i4i22-2-2-222−22−2222222i22i2−2i2−2i200000022−22−2i22i2000−2i2i2i−2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
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χ7244-4-4-4400-200−4i4i4i−4i22-2-2-222−22−222222−2i2−2i22i22i200000022−222i2−2i20002i−2i−2i2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
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χ804-44-400-4440000000000-44-42i2−2i22i2−2i2−2i22i2−2i22i200-44000000000000002i2−2i22i2−2i20000−2i22i2−2i22i2000000000000000000000000000000000000
χ814-44-400-44-2000000−2i32i3−2i32i32-22−2i22i2−2i22i22i2−2i22i2−2i2002-22i3−2i3000000000000i2−i2i2−i26−66−6−i2i2−i2i2−66−6600000000000000000000000000000000
χ824-44-400-44-2000000−2i32i3−2i32i32-222i2−2i22i2−2i2−2i22i2−2i22i2002-22i3−2i3000000000000−i2i2−i2i2−66−66i2−i2i2−i26−66−600000000000000000000000000000000
χ834-44-400-44-20000002i3−2i32i3−2i32-22−2i22i2−2i22i22i2−2i22i2−2i2002-2−2i32i3000000000000i2−i2i2−i2−66−66−i2i2−i2i26−66−600000000000000000000000000000000
χ844-44-400-44-20000002i3−2i32i3−2i32-222i2−2i22i2−2i2−2i22i2−2i22i2002-2−2i32i3000000000000−i2i2−i2i26−66−6i2−i2i2−i2−66−6600000000000000000000000000000000
χ854-4-44000044-400000000-4-444i−4i−4i4i000000000000004000000-44i−4i−4i4i00000000000000000000000000000000000000000000
χ864-4-44000044-400000000-4-44−4i4i4i−4i000000000000004000000-4−4i4i4i−4i00000000000000000000000000000000000000000000
χ874-4-4400004-4400000000-4-4400004-4-440000000000-40000004000000004-4-44000000000000000000000000000000000000
χ884-4-4400004-4400000000-4-440000-444-40000000000-4000000400000000-444-4000000000000000000000000000000000000
χ894-4-440000-24-40000−2i32i32i3−2i322-24i−4i−4i4i00000000000000-2−2i32i300002−2i2i2i−2i−232323−230000000000000000000000000000000000000000
χ904-4-440000-24-40000−2i32i32i3−2i322-2−4i4i4i−4i00000000000000-2−2i32i3000022i−2i−2i2i23−23−23230000000000000000000000000000000000000000
χ914-4-440000-24-400002i3−2i3−2i32i322-24i−4i−4i4i00000000000000-22i3−2i300002−2i2i2i−2i23−23−23230000000000000000000000000000000000000000
χ924-4-440000-24-400002i3−2i3−2i32i322-2−4i4i4i−4i00000000000000-22i3−2i3000022i−2i−2i2i−232323−230000000000000000000000000000000000000000
χ934-4-440000-2-440000−2i32i32i3−2i322-200004-4-44000000000022i3−2i30000-200000000-222-22i3−2i3−2i32i300000000000000000000000000000000
χ944-4-440000-2-440000−2i32i32i3−2i322-20000-444-4000000000022i3−2i30000-2000000002-2-22−2i32i32i3−2i300000000000000000000000000000000
χ954-4-440000-2-4400002i3−2i3−2i32i322-200004-4-4400000000002−2i32i30000-200000000-222-2−2i32i32i3−2i300000000000000000000000000000000
χ964-4-440000-2-4400002i3−2i3−2i32i322-20000-444-400000000002−2i32i30000-2000000002-2-222i3−2i3−2i32i300000000000000000000000000000000

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