Finite Group Databasebeta

← Group #10694566

Character table — Group #10694566

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order1222223444444446668888888812121212446688881212121212121212121224242424242424242424242424242424888888888888888822446666121212124444
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
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111-1-11111-1-1
χ91111-1-11-1-111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11111-1-1-1-1i−ii−i
χ101111-1-11-1-111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-1-1-11111−ii−ii
χ111111-1-11-1-111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11111-1-1-1-1−ii−ii
χ121111-1-11-1-111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1-1-11111i−ii−i
χ131111-1-11-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111i−i−ii
χ141111-1-11-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−iii−i
χ151111-1-11-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−iii−i
χ161111-1-11-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1i−i−ii
χ1722222222222-2-2-2-22222222-2-2-2-22222-2-222-2-222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-222222222-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ192222222-2-2-2-222-2-222200000000-2-2-2-22-222000022-2-222-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ202222222-2-2-2-222-2-222200000000-2-2-2-22-222000022-2-222-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ212222222-2-2-2-2-2-22222200000000-2-2-2-2-22220000-2-222-2-222-2-2000000000000000022-2-222-2-2000000000000000000000000
χ222222222-2-2-2-2-2-22222200000000-2-2-2-2-22220000-2-222-2-222-2-20000000000000000-2-222-2-222000000000000000000000000
χ23222222-122222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ24222222-122222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ25222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000002-22-2-1-111-1-1110000
χ26222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-22-2211-1-111-1-10000
χ27222222-12222-2-2-2-2-1-1-12222-2-2-2-2-1-1-1-1-2-2-1-1-2-22211111111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ28222222-12222-2-2-2-2-1-1-12222-2-2-2-2-1-1-1-1-2-2-1-1-2-22211111111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ29222222-12222-2-2-2-2-1-1-1-2-2-2-22222-1-1-1-1-2-2-1-122-2-211111111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ30222222-12222-2-2-2-2-1-1-1-2-2-2-22222-1-1-1-1-2-2-1-122-2-211111111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ312222-2-2222-2-222-2-2222000000002222-22-2-20000-2-22222-2-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ322222-2-2222-2-222-2-2222000000002222-22-2-20000-2-22222-2-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ332222-2-2222-2-2-2-2222220000000022222-2-2-2000022-2-2-2-222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ342222-2-2222-2-2-2-2222220000000022222-2-2-2000022-2-2-2-222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ352222-2-22-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ362222-2-22-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ372222-2-2-1-2-2222222-1-1-1222222221111-2-211-2-2-2-21111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ382222-2-2-1-2-2222222-1-1-1222222221111-2-211-2-2-2-21111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ392222-2-2-1-2-2222222-1-1-1-2-2-2-2-2-2-2-21111-2-21122221111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ402222-2-2-1-2-2222222-1-1-1-2-2-2-2-2-2-2-21111-2-21122221111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ412222-2-2-1-2-222-2-2-2-2-1-1-12222-2-2-2-21111221122-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ422222-2-2-1-2-222-2-2-2-2-1-1-12222-2-2-2-21111221122-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ432222-2-2-1-2-222-2-2-2-2-1-1-1-2-2-2-2222211112211-2-222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ442222-2-2-1-2-222-2-2-2-2-1-1-1-2-2-2-2222211112211-2-222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ452-2-222-222-22-20000-2-22000022-2-222-2-2002-22-200000000002-2000022-2-2000022-2-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ462-2-222-222-22-20000-2-22000022-2-222-2-2002-22-200000000002-2000022-2-2000022-2-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ472-2-222-222-22-20000-2-220000-2-22222-2-2002-2-2200000000002-20000-2-2220000-2-222−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ482-2-222-222-22-20000-2-220000-2-22222-2-2002-2-2200000000002-20000-2-2220000-2-222i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ492-2-222-22-22-220000-2-2222-2-20000-2-222002-2002-200000000-2222-2-2000022-2-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ502-2-222-22-22-220000-2-2222-2-20000-2-222002-2002-200000000-2222-2-2000022-2-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ512-2-222-22-22-220000-2-22-2-2220000-2-222002-200-2200000000-22-2-2220000-2-2220000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ522-2-222-22-22-220000-2-22-2-2220000-2-222002-200-2200000000-22-2-2220000-2-2220000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ532-2-22-2222-2-220000-2-2222-2-2000022-2-200-2200-2200000000-2222-2-20000-2-22200002−2−22−222−22−2−22−222−20000000000000000
χ542-2-22-2222-2-220000-2-2222-2-2000022-2-200-2200-2200000000-2222-2-20000-2-2220000−222−22−2−22−222−22−2−220000000000000000
χ552-2-22-2222-2-220000-2-22-2-222000022-2-200-22002-200000000-22-2-222000022-2-200002−2−22−222−2−222−22−2−220000000000000000
χ562-2-22-2222-2-220000-2-22-2-222000022-2-200-22002-200000000-22-2-222000022-2-20000−222−22−2−222−2−22−222−20000000000000000
χ572-2-22-222-222-20000-2-22000022-2-2-2-22200-22-2200000000002-20000-2-222000022-2-22−22−2−22−22−22−222−22−20000000000000000
χ582-2-22-222-222-20000-2-22000022-2-2-2-22200-22-2200000000002-20000-2-222000022-2-2−22−222−22−22−22−2−22−220000000000000000
χ592-2-22-222-222-20000-2-220000-2-222-2-22200-222-200000000002-2000022-2-20000-2-2222−22−2−22−222−22−2−22−220000000000000000
χ602-2-22-222-222-20000-2-220000-2-222-2-22200-222-200000000002-2000022-2-20000-2-222−22−222−22−2−22−222−22−20000000000000000
χ61444444-2-4-4-4-444-4-4-2-2-20000000022224-4-2-20000-2-222-2-22222000000000000000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-444-2-2-2000000002222-44-2-2000022-2-222-2-222000000000000000000000000000000000000000000000000
χ634444-4-4-244-4-444-4-4-2-2-200000000-2-2-2-2-4422000022-2-2-2-22222000000000000000000000000000000000000000000000000
χ644444-4-4-244-4-4-4-444-2-2-200000000-2-2-2-24-4220000-2-22222-2-222000000000000000000000000000000000000000000000000
χ6544-4-40040000004i−4i4-4-422−2222−22−2i22i2−2i22i20000000000000000004i−4i0022−2222−2200000000−2i22i2−2i22i200000000000000000000000000000000
χ6644-4-40040000004i−4i4-4-4−2222−22222i2−2i22i2−2i20000000000000000004i−4i00−2222−2222000000002i2−2i22i2−2i200000000000000000000000000000000
χ6744-4-4004000000−4i4i4-4-422−2222−222i2−2i22i2−2i2000000000000000000−4i4i0022−2222−22000000002i2−2i22i2−2i200000000000000000000000000000000
χ6844-4-4004000000−4i4i4-4-4−2222−2222−2i22i2−2i22i2000000000000000000−4i4i00−2222−222200000000−2i22i2−2i22i200000000000000000000000000000000
χ6944-4-400-20000004i−4i-22222−2222−22−2i22i2−2i22i223−2323−2300000000−2i32i30000−2i2i00−22−22i6−i6i6−i66−66−6i2−i2i2−i200000000000000000000000000000000
χ7044-4-400-20000004i−4i-22222−2222−22−2i22i2−2i22i2−2323−2323000000002i3−2i30000−2i2i00−22−22−i6i6−i6i6−66−66i2−i2i2−i200000000000000000000000000000000
χ7144-4-400-20000004i−4i-222−2222−22222i2−2i22i2−2i223−2323−2300000000−2i32i30000−2i2i002−22−2−i6i6−i6i6−66−66−i2i2−i2i200000000000000000000000000000000
χ7244-4-400-20000004i−4i-222−2222−22222i2−2i22i2−2i2−2323−2323000000002i3−2i30000−2i2i002−22−2i6−i6i6−i66−66−6−i2i2−i2i200000000000000000000000000000000
χ7344-4-400-2000000−4i4i-22222−2222−222i2−2i22i2−2i223−2323−23000000002i3−2i300002i−2i00−22−22−i6i6−i6i66−66−6−i2i2−i2i200000000000000000000000000000000
χ7444-4-400-2000000−4i4i-22222−2222−222i2−2i22i2−2i2−2323−232300000000−2i32i300002i−2i00−22−22i6−i6i6−i6−66−66−i2i2−i2i200000000000000000000000000000000
χ7544-4-400-2000000−4i4i-222−2222−2222−2i22i2−2i22i223−2323−23000000002i3−2i300002i−2i002−22−2i6−i6i6−i6−66−66i2−i2i2−i200000000000000000000000000000000
χ7644-4-400-2000000−4i4i-222−2222−2222−2i22i2−2i22i2−2323−232300000000−2i32i300002i−2i002−22−2−i6i6−i6i66−66−6i2−i2i2−i200000000000000000000000000000000
χ774-44-400400004i−4i00-44-422−22−2222−2i22i22i2−2i200000000000000004i−4i000022−22−222200000000−2i22i22i2−2i200000000000000000000000000000000
χ784-44-400400004i−4i00-44-4−222222−222i2−2i2−2i22i200000000000000004i−4i0000−222222−22000000002i2−2i2−2i22i200000000000000000000000000000000
χ794-44-40040000−4i4i00-44-422−22−22222i2−2i2−2i22i20000000000000000−4i4i000022−22−2222000000002i2−2i2−2i22i200000000000000000000000000000000
χ804-44-40040000−4i4i00-44-4−222222−22−2i22i22i2−2i20000000000000000−4i4i0000−222222−2200000000−2i22i22i2−2i200000000000000000000000000000000
χ814-44-400-200004i−4i002-2222−22−2222−2i22i22i2−2i223−23−23230000000000−2i32i3−2i2i0000−222−2i6−i6−i6i6−666−6i2−i2−i2i200000000000000000000000000000000
χ824-44-400-200004i−4i002-2222−22−2222−2i22i22i2−2i2−232323−2300000000002i3−2i3−2i2i0000−222−2−i6i6i6−i66−6−66i2−i2−i2i200000000000000000000000000000000
χ834-44-400-200004i−4i002-22−222222−222i2−2i2−2i22i223−23−23230000000000−2i32i3−2i2i00002−2−22−i6i6i6−i66−6−66−i2i2i2−i200000000000000000000000000000000
χ844-44-400-200004i−4i002-22−222222−222i2−2i2−2i22i2−232323−2300000000002i3−2i3−2i2i00002−2−22i6−i6−i6i6−666−6−i2i2i2−i200000000000000000000000000000000
χ854-44-400-20000−4i4i002-2222−22−22222i2−2i2−2i22i223−23−232300000000002i3−2i32i−2i0000−222−2−i6i6i6−i6−666−6−i2i2i2−i200000000000000000000000000000000
χ864-44-400-20000−4i4i002-2222−22−22222i2−2i2−2i22i2−232323−230000000000−2i32i32i−2i0000−222−2i6−i6−i6i66−6−66−i2i2i2−i200000000000000000000000000000000
χ874-44-400-20000−4i4i002-22−222222−22−2i22i22i2−2i223−23−232300000000002i3−2i32i−2i00002−2−22i6−i6−i6i66−6−66i2−i2−i2i200000000000000000000000000000000
χ884-44-400-20000−4i4i002-22−222222−22−2i22i22i2−2i2−232323−230000000000−2i32i32i−2i00002−2−22−i6i6i6−i6−666−6i2−i2−i2i200000000000000000000000000000000
χ894-4-444-4-24-44-4000022-2000044-4-4-2-22200-224-40000000000-220000-2-2220000-2-22200000000000000000000000000000000
χ904-4-444-4-24-44-4000022-20000-4-444-2-22200-22-440000000000-22000022-2-2000022-2-200000000000000000000000000000000
χ914-4-444-4-2-44-44000022-244-4-4000022-2-200-22004-4000000002-2-2-2220000-2-222000000000000000000000000000000000000
χ924-4-444-4-2-44-44000022-2-4-444000022-2-200-2200-44000000002-222-2-2000022-2-2000000000000000000000000000000000000
χ934-4-44-44-24-4-44000022-244-4-40000-2-222002-200-44000000002-2-2-222000022-2-2000000000000000000000000000000000000
χ944-4-44-44-24-4-44000022-2-4-4440000-2-222002-2004-4000000002-222-2-20000-2-222000000000000000000000000000000000000
χ954-4-44-44-2-444-4000022-2000044-4-422-2-2002-2-440000000000-22000022-2-20000-2-22200000000000000000000000000000000
χ964-4-44-44-2-444-4000022-20000-4-44422-2-2002-24-40000000000-220000-2-222000022-2-200000000000000000000000000000000

Here i is the imaginary unit (i² = −1).