Finite Group Databasebeta

← Group #10694787

Character table — Group #10694787

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12222234444444466666668888888844888812121212121212121212121224242424242424242424242424242424888888888888888822446666121212128888
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
χ51111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111111-111-1-1-1-1-111111111111-1-1-1-11-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-111-1-1i−ii−i
χ101111111-111-1-1-1-1-111111111111-1-1-1-11-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111-1-111−ii−ii
χ111111111-111-1-1-1-1-111111111111-1-1-1-11-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-111-1-1−ii−ii
χ121111111-111-1-1-1-1-111111111111-1-1-1-11-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111-1-111i−ii−i
χ131111111-111-1-1-1-1-11111111-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111i−i−ii
χ141111111-111-1-1-1-1-11111111-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−iii−i
χ151111111-111-1-1-1-1-11111111-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−iii−i
χ161111111-111-1-1-1-1-11111111-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1i−i−ii
χ1722222222-2-2-2-2222222222200000000-2-20000-2-2-2-2-2-22222-2-200000000000000000000000022-2-222-2-20000000000000000
χ1822222222-2-2-2-2222222222200000000-2-20000-2-2-2-2-2-22222-2-2000000000000000000000000-2-222-2-2220000000000000000
χ192222222-2-2-222-2-2-2222222200000000-220000-2-22222-2-2-2-2-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ202222222-2-2-222-2-2-2222222200000000-220000-2-22222-2-2-2-2-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ21222222-122222222-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ22222222-122222222-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ23222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ24222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ25222222-1-222-2-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-22-222-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111100000000000000002-22-2-1-111-1-1110000
χ26222222-1-222-2-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-22-222-2-2-1-111111111-1-1-1-1-1-1-1-1-1-1111111110000000000000000-22-2211-1-111-1-10000
χ27222222-1-222-2-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222222-2-2-222-1-111111111-1-111111111-1-1-1-1-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ28222222-1-222-2-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222222-2-2-222-1-111111111-1-111111111-1-1-1-1-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ292222-2-22222-2-2-2-22-2-2-2-22222222-2-2-2-2-22-2-222-2-222-2-222-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ302222-2-22222-2-2-2-22-2-2-2-2222-2-2-2-22222-2222-2-2-2-222-2-222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ312222-2-222-2-222-2-22-2-2-2-2222000000002-2000022-2-22222-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ322222-2-222-2-222-2-22-2-2-2-2222000000002-2000022-2-22222-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ332222-2-22-2222222-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-222-2-222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ342222-2-22-2222222-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222-2-22222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ352222-2-22-2-2-2-2-222-2-2-2-2-2222000000002200002222-2-2-2-222-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ362222-2-22-2-2-2-2-222-2-2-2-2-2222000000002200002222-2-2-2-222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ372222-2-2-1222-2-2-2-221111-1-1-12222-2-2-2-2-22-2-22211-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ382222-2-2-1222-2-2-2-221111-1-1-12222-2-2-2-2-22-2-22211-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ392222-2-2-1222-2-2-2-221111-1-1-1-2-2-2-22222-2222-2-211-1-111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ402222-2-2-1222-2-2-2-221111-1-1-1-2-2-2-22222-2222-2-211-1-111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ412222-2-2-1-2222222-21111-1-1-122222222-2-2-2-2-2-21111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ422222-2-2-1-2222222-21111-1-1-122222222-2-2-2-2-2-21111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ432222-2-2-1-2222222-21111-1-1-1-2-2-2-2-2-2-2-2-2-222221111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ442222-2-2-1-2222222-21111-1-1-1-2-2-2-2-2-2-2-2-2-222221111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ452-2-222-22200002-2-222-2-2-2-2222−2−222−2−2002−22−20000002-22-20022−2−222−2−222−2−222−2−2−i2i2−i2i2−i2i2−i2i2002i−2i002i−2i0000000000000000
χ462-2-222-22200002-2-222-2-2-2-2222−2−222−2−2002−22−20000002-22-20022−2−222−2−222−2−222−2−2i2−i2i2−i2i2−i2i2−i200−2i2i00−2i2i0000000000000000
χ472-2-222-22200002-2-222-2-2-2-22−2−222−2−22200−22−220000002-22-200−2−222−2−222−2−222−2−222−i2i2−i2i2−i2i2−i2i200−2i2i00−2i2i0000000000000000
χ482-2-222-22200002-2-222-2-2-2-22−2−222−2−22200−22−220000002-22-200−2−222−2−222−2−222−2−222i2−i2i2−i2i2−i2i2−i2002i−2i002i−2i0000000000000000
χ492-2-222-22-20000-22222-2-2-2-2222−2−2−2−222002−2−22000000-22-220022−2−222−2−2−2−222−2−2222−22−2−22−2200-22002-20000000000000000
χ502-2-222-22-20000-22222-2-2-2-2222−2−2−2−222002−2−22000000-22-220022−2−222−2−2−2−222−2−222−22−222−22−2002-200-220000000000000000
χ512-2-222-22-20000-22222-2-2-2-22−2−22222−2−200−222−2000000-22-2200−2−222−2−22222−2−222−2−22−22−2−22−22002-200-220000000000000000
χ522-2-222-22-20000-22222-2-2-2-22−2−22222−2−200−222−2000000-22-2200−2−222−2−22222−2−222−2−2−22−222−22−200-22002-20000000000000000
χ532-2-22-22220000-22-2-2-222-2-2222−2−2−2−22200−222−20000002-2-220022−2−2−2−22222−2−2−2−222−i2i2i2−i2−i2i2i2−i22i−2i002i−2i000000000000000000
χ542-2-22-22220000-22-2-2-222-2-2222−2−2−2−22200−222−20000002-2-220022−2−2−2−22222−2−2−2−222i2−i2−i2i2i2−i2−i2i2−2i2i00−2i2i000000000000000000
χ552-2-22-22220000-22-2-2-222-2-22−2−22222−2−2002−2−220000002-2-2200−2−22222−2−2−2−22222−2−2−i2i2i2−i2−i2i2i2−i2−2i2i00−2i2i000000000000000000
χ562-2-22-22220000-22-2-2-222-2-22−2−22222−2−2002−2−220000002-2-2200−2−22222−2−2−2−22222−2−2i2−i2−i2i2i2−i2−i2i22i−2i002i−2i000000000000000000
χ572-2-22-222-200002-22-2-222-2-2222−2−222−2−200−22−22000000-222-20022−2−2−2−222−2−22222−2−22−2−22−222−2-22002-2000000000000000000
χ582-2-22-222-200002-22-2-222-2-2222−2−222−2−200−22−22000000-222-20022−2−2−2−222−2−22222−2−2−222−22−2−222-200-22000000000000000000
χ592-2-22-222-200002-22-2-222-2-22−2−222−2−222002−22−2000000-222-200−2−22222−2−222−2−2−2−2222−2−22−222−22-200-22000000000000000000
χ602-2-22-222-200002-22-2-222-2-22−2−222−2−222002−22−2000000-222-200−2−22222−2−222−2−2−2−222−222−22−2−22-22002-2000000000000000000
χ61444444-24-4-4-4-4444-2-2-2-2-2-2-200000000-4-40000222222-2-2-2-222000000000000000000000000000000000000000000000000
χ62444444-2-4-4-444-4-4-4-2-2-2-2-2-2-200000000-44000022-2-2-2-2222222000000000000000000000000000000000000000000000000
χ634444-4-4-24-4-444-4-442222-2-2-2000000004-40000-2-222-2-2-2-22222000000000000000000000000000000000000000000000000
χ644444-4-4-2-4-4-4-4-444-42222-2-2-200000000440000-2-2-2-22222-2-222000000000000000000000000000000000000000000000000
χ6544-4-40040004-400000004-4-4−2i22i2−2i22i2−2i22i2−2i22i200000000004-4000000−2i22i2−2i22i200000000−2i22i2−2i22i200000000000000000000000000000000
χ6644-4-40040004-400000004-4-42i2−2i22i2−2i22i2−2i22i2−2i200000000004-40000002i2−2i22i2−2i2000000002i2−2i22i2−2i200000000000000000000000000000000
χ6744-4-4004000-4400000004-4-4−2i22i2−2i22i22i2−2i22i2−2i20000000000-44000000−2i22i2−2i22i2000000002i2−2i22i2−2i200000000000000000000000000000000
χ6844-4-4004000-4400000004-4-42i2−2i22i2−2i2−2i22i2−2i22i20000000000-440000002i2−2i22i2−2i200000000−2i22i2−2i22i200000000000000000000000000000000
χ6944-4-400-20004-4000−2i32i3−2i32i3-222−2i22i2−2i22i2−2i22i2−2i22i200000000−2i32i3-22000000i2−i2i2−i26−66−66−66−6i2−i2i2−i200000000000000000000000000000000
χ7044-4-400-20004-4000−2i32i3−2i32i3-2222i2−2i22i2−2i22i2−2i22i2−2i200000000−2i32i3-22000000−i2i2−i2i2−66−66−66−66−i2i2−i2i200000000000000000000000000000000
χ7144-4-400-20004-40002i3−2i32i3−2i3-222−2i22i2−2i22i2−2i22i2−2i22i2000000002i3−2i3-22000000i2−i2i2−i2−66−66−66−66i2−i2i2−i200000000000000000000000000000000
χ7244-4-400-20004-40002i3−2i32i3−2i3-2222i2−2i22i2−2i22i2−2i22i2−2i2000000002i3−2i3-22000000−i2i2−i2i26−66−66−66−6−i2i2−i2i200000000000000000000000000000000
χ7344-4-400-2000-44000−2i32i3−2i32i3-222−2i22i2−2i22i22i2−2i22i2−2i2000000002i3−2i32-2000000i2−i2i2−i26−66−6−66−66−i2i2−i2i200000000000000000000000000000000
χ7444-4-400-2000-44000−2i32i3−2i32i3-2222i2−2i22i2−2i2−2i22i2−2i22i2000000002i3−2i32-2000000−i2i2−i2i2−66−666−66−6i2−i2i2−i200000000000000000000000000000000
χ7544-4-400-2000-440002i3−2i32i3−2i3-222−2i22i2−2i22i22i2−2i22i2−2i200000000−2i32i32-2000000i2−i2i2−i2−66−666−66−6−i2i2−i2i200000000000000000000000000000000
χ7644-4-400-2000-440002i3−2i32i3−2i3-2222i2−2i22i2−2i2−2i22i2−2i22i200000000−2i32i32-2000000−i2i2−i2i26−66−6−66−66i2−i2i2−i200000000000000000000000000000000
χ774-44-400404-4000000000-44-400004i−4i−4i4i00000000000000004-40000000000004i−4i−4i4i00000000000000000000000000000000
χ784-44-400404-4000000000-44-40000−4i4i4i−4i00000000000000004-4000000000000−4i4i4i−4i00000000000000000000000000000000
χ794-44-40040-44000000000-44-44i−4i−4i4i00000000000000000000-444i−4i−4i4i00000000000000000000000000000000000000000000
χ804-44-40040-44000000000-44-4−4i4i4i−4i00000000000000000000-44−4i4i4i−4i00000000000000000000000000000000000000000000
χ814-44-400-204-400000−2i32i32i3−2i32-2200004i−4i−4i4i000000−2i32i300000000-2200000000−232323−23−2i2i2i−2i00000000000000000000000000000000
χ824-44-400-204-400000−2i32i32i3−2i32-220000−4i4i4i−4i000000−2i32i300000000-220000000023−23−23232i−2i−2i2i00000000000000000000000000000000
χ834-44-400-204-4000002i3−2i3−2i32i32-2200004i−4i−4i4i0000002i3−2i300000000-220000000023−23−2323−2i2i2i−2i00000000000000000000000000000000
χ844-44-400-204-4000002i3−2i3−2i32i32-220000−4i4i4i−4i0000002i3−2i300000000-2200000000−232323−232i−2i−2i2i00000000000000000000000000000000
χ854-44-400-20-4400000−2i32i32i3−2i32-224i−4i−4i4i00000000002i3−2i3000000002-2−2i2i2i−2i−232323−230000000000000000000000000000000000000000
χ864-44-400-20-4400000−2i32i32i3−2i32-22−4i4i4i−4i00000000002i3−2i3000000002-22i−2i−2i2i23−23−23230000000000000000000000000000000000000000
χ874-44-400-20-44000002i3−2i3−2i32i32-224i−4i−4i4i0000000000−2i32i3000000002-2−2i2i2i−2i23−23−23230000000000000000000000000000000000000000
χ884-44-400-20-44000002i3−2i3−2i32i32-22−4i4i4i−4i0000000000−2i32i3000000002-22i−2i−2i2i−232323−230000000000000000000000000000000000000000
χ894-4-444-4-2400004-4-4-2-22222-22222−22−222222−22−220022−2222−22000000-22-2200−2−222−2−222−2−222−2−22200000000000000000000000000000000
χ904-4-444-4-2400004-4-4-2-22222-2−22−222222−22−22222200−2222−2222000000-22-220022−2−222−2−222−2−222−2−200000000000000000000000000000000
χ914-4-444-4-2-40000-444-2-22222-22222−22−22−22−2222220022−22−22220000002-22-200−2−222−2−22222−2−222−2−200000000000000000000000000000000
χ924-4-444-4-2-40000-444-2-22222-2−22−2222222222−22−2200−222222−220000002-22-20022−2−222−2−2−2−222−2−22200000000000000000000000000000000
χ934-4-44-44-240000-44-422-2-222-22222−22−22−22−22222200−222222−22000000-222-200−2−22222−2−2−2−22222−2−200000000000000000000000000000000
χ944-4-44-44-240000-44-422-2-222-2−22−2222222222−22−220022−22−2222000000-222-20022−2−2−2−22222−2−2−2−22200000000000000000000000000000000
χ954-4-44-44-2-400004-4422-2-222-22222−22−222222−22−2200−2222−22220000002-2-2200−2−22222−2−222−2−2−2−22200000000000000000000000000000000
χ964-4-44-44-2-400004-4422-2-222-2−22−222222−22−2222220022−2222−220000002-2-220022−2−2−2−222−2−22222−2−200000000000000000000000000000000

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