Finite Group Databasebeta

← Group #10697965

Character table — Group #10697965

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12222222344444444444466666668888888812121212121212121212121224242424242424242424242424242424888888888888888822446666121212124444
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ922222222222-2-2-2-222-2-2-2-222222222222-2-2-2-222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1022222222222-2-2-2-222-2-2-2-22222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ11222222222-2-222-2-2-2-222-2-2222222200000000-2-22222-2-2-2-2-2-20000000000000000000000002222-2-2-2-20000000000000000
χ12222222222-2-222-2-2-2-222-2-2222222200000000-2-22222-2-2-2-2-2-2000000000000000000000000-2-2-2-222220000000000000000
χ13222222222-2-2-2-222-2-2-2-222222222200000000-2-2-2-2-2-22222-2-200000000000000002222-2-2-2-2000000000000000000000000
χ14222222222-2-2-2-222-2-2-2-222222222200000000-2-2-2-2-2-22222-2-20000000000000000-2-2-2-22222000000000000000000000000
χ1522222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ1622222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ1722222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ1822222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ1922222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111100000000000000000000−i3−i3i3i3−i3−i3i3i30000
χ2022222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111100000000000000000000i3i3−i3−i3i3i3−i3−i30000
χ2122222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000−i3−i3i3i3i3i3−i3−i30000
χ2222222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000i3i3−i3−i3−i3−i3i3i30000
χ2322-2-22-22-22002-200002-20022-2-22-2-2−i2−i2i2i2−i2−i2i2i20022-2-2000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i222−2−222−2−200002i2i−2i−2i0000000000000000
χ2422-2-22-22-22002-200002-20022-2-22-2-2−i2−i2i2i2−i2−i2i2i20022-2-2000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−2−222−2−2220000−2i−2i2i2i0000000000000000
χ2522-2-22-22-22002-200002-20022-2-22-2-2i2i2−i2−i2i2i2−i2−i20022-2-2000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i222−2−222−2−20000−2i−2i2i2i0000000000000000
χ2622-2-22-22-22002-200002-20022-2-22-2-2i2i2−i2−i2i2i2−i2−i20022-2-2000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2−2−222−2−22200002i2i−2i−2i0000000000000000
χ2722-2-22-22-2200-220000-220022-2-22-2-2−i2−i2i2i2i2i2−i2−i200-2-222000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i222−2−2−2−2222i2i−2i−2i00000000000000000000
χ2822-2-22-22-2200-220000-220022-2-22-2-2−i2−i2i2i2i2i2−i2−i200-2-222000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2−2−22222−2−2−2i−2i2i2i00000000000000000000
χ2922-2-22-22-2200-220000-220022-2-22-2-2i2i2−i2−i2−i2−i2i2i200-2-222000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i222−2−2−2−222−2i−2i2i2i00000000000000000000
χ3022-2-22-22-2200-220000-220022-2-22-2-2i2i2−i2−i2−i2−i2i2i200-2-222000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2−2−22222−2−22i2i−2i−2i00000000000000000000
χ312-22-2-222-222-200002-200002-22-2-22-200002i−2i2i−2i2-2000000002-2000000002i2i−2i−2i2i2i−2i−2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ322-22-2-222-222-200002-200002-22-2-22-200002i−2i2i−2i2-2000000002-2000000002i2i−2i−2i2i2i−2i−2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ332-22-2-222-222-200002-200002-22-2-22-20000−2i2i−2i2i2-2000000002-200000000−2i−2i2i2i−2i−2i2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ342-22-2-222-222-200002-200002-22-2-22-20000−2i2i−2i2i2-2000000002-200000000−2i−2i2i2i−2i−2i2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ352-22-2-222-22-220000-2200002-22-2-22-22i−2i2i−2i0000-2200000000-222i2i−2i−2i2i2i−2i−2i000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ362-22-2-222-22-220000-2200002-22-2-22-22i−2i2i−2i0000-2200000000-222i2i−2i−2i2i2i−2i−2i00000000−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ372-22-2-222-22-220000-2200002-22-2-22-2−2i2i−2i2i0000-2200000000-22−2i−2i2i2i−2i−2i2i2i000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ382-22-2-222-22-220000-2200002-22-2-22-2−2i2i−2i2i0000-2200000000-22−2i−2i2i2i−2i−2i2i2i00000000−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ392-2-22-2-222200002-200002-22-2-22-2-222−2−222−2−2200000022-2-20022−2−2−2−22222−2−2−2−22200002-2-222−2−222−2−220000000000000000
χ402-2-22-2-222200002-200002-22-2-22-2-222−2−222−2−2200000022-2-20022−2−2−2−22222−2−2−2−2220000-222-2−222−2−222−20000000000000000
χ412-2-22-2-222200002-200002-22-2-22-2-22−222−2−222−200000022-2-200−2−22222−2−2−2−22222−2−200002-2-22−222−2−222−20000000000000000
χ422-2-22-2-222200002-200002-22-2-22-2-22−222−2−222−200000022-2-200−2−22222−2−2−2−22222−2−20000-222-22−2−222−2−220000000000000000
χ432-2-22-2-22220000-220000-222-2-22-2-222−2−22−222−2000000-2-2220022−2−2−2−222−2−22222−2−22-2-2200002−2−22−222−20000000000000000
χ442-2-22-2-22220000-220000-222-2-22-2-222−2−22−222−2000000-2-2220022−2−2−2−222−2−22222−2−2-222-20000−222−22−2−220000000000000000
χ452-2-22-2-22220000-220000-222-2-22-2-22−222−22−2−22000000-2-22200−2−22222−2−222−2−2−2−2222-2-220000−222−22−2−220000000000000000
χ462-2-22-2-22220000-220000-222-2-22-2-22−222−22−2−22000000-2-22200−2−22222−2−222−2−2−2−222-222-200002−2−22−222−20000000000000000
χ472-2-2-222-222222222-2-2-2-2-2-2-2-2-2-222200000000222-22-22-22-2-2-2000000000000000000000000000000000000000000002i−2i00
χ482-2-2-222-222222222-2-2-2-2-2-2-2-2-2-222200000000222-22-22-22-2-2-200000000000000000000000000000000000000000000−2i2i00
χ492-2-2-222-22222-2-2-2-2-2-22222-2-2-2-22220000000022-22-22-22-22-2-200000000000000000000000000000000000000000000002-2
χ502-2-2-222-22222-2-2-2-2-2-22222-2-2-2-22220000000022-22-22-22-22-2-20000000000000000000000000000000000000000000000-22
χ512-2-2-222-222-2-222-2-222-2-222-2-2-2-222200000000-2-22-22-2-22-222200000000000000000000000000000000002-200002-22-20000
χ522-2-2-222-222-2-222-2-222-2-222-2-2-2-222200000000-2-22-22-2-22-22220000000000000000000000000000000000-220000-22-220000
χ532-2-2-222-222-2-2-2-2222222-2-2-2-2-2-222200000000-2-2-22-222-22-222000000000000000000000000000000002-2002-22-200000000
χ542-2-2-222-222-2-2-2-2222222-2-2-2-2-2-222200000000-2-2-22-222-22-22200000000000000000000000000000000-2200-22-2200000000
χ552-2-2-222-22-1-2-222-2-222-2-2221111-1-1-10000000011-11-111-11-1-1-1−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000000002-2−i3i3i3−i3-11-110000
χ562-2-2-222-22-1-2-222-2-222-2-2221111-1-1-10000000011-11-111-11-1-1-1−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000000-22i3−i3−i3i31-11-10000
χ572-2-2-222-22-1-2-222-2-222-2-2221111-1-1-10000000011-11-111-11-1-1-1i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000000002-2i3−i3−i3i3-11-110000
χ582-2-2-222-22-1-2-222-2-222-2-2221111-1-1-10000000011-11-111-11-1-1-1i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000000-22−i3i3i3−i31-11-10000
χ592-2-2-222-22-1-2-2-2-2222222-2-21111-1-1-100000000111-11-1-11-11-1-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i300000000000000002-200-11-11−i3i3i3−i30000
χ602-2-2-222-22-1-2-2-2-2222222-2-21111-1-1-100000000111-11-1-11-11-1-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000000000000000-22001-11-1i3−i3−i3i30000
χ612-2-2-222-22-1-2-2-2-2222222-2-21111-1-1-100000000111-11-1-11-11-1-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i300000000000000002-200-11-11i3−i3−i3i30000
χ622-2-2-222-22-1-2-2-2-2222222-2-21111-1-1-100000000111-11-1-11-11-1-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000000000000000-22001-11-1−i3i3i3−i30000
χ6344444444-2-4-444-4-4-4-444-4-4-2-2-2-2-2-2-20000000022-2-2-2-2222222000000000000000000000000000000000000000000000000
χ6444444444-2-4-4-4-444-4-4-4-444-2-2-2-2-2-2-200000000222222-2-2-2-222000000000000000000000000000000000000000000000000
χ65444-4-4-4-44400004-40000-44-444-4-4-44000000000000004-4-4400000000000000000000000000000000000000000000000000
χ66444-4-4-4-4440000-4400004-4-444-4-4-4400000000000000-444-400000000000000000000000000000000000000000000000000
χ67444-4-4-4-44-200004-40000-442-2-2222-200000000000000-222-200i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000
χ68444-4-4-4-44-200004-40000-442-2-2222-200000000000000-222-200−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000
χ69444-4-4-4-44-20000-4400004-42-2-2222-2000000000000002-2-2200i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000
χ70444-4-4-4-44-20000-4400004-42-2-2222-2000000000000002-2-2200−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000
χ7144-44-44-4-444-40000-440000-44-44-44-4000000004-400000000-44000000000000000000000000000000000000000000000000
χ7244-44-44-4-44-4400004-40000-44-44-44-400000000-44000000004-4000000000000000000000000000000000000000000000000
χ7344-44-44-4-4-24-40000-4400002-22-22-2200000000-22000000002-223−23−232323−23−23230000000000000000000000000000000000000000
χ7444-44-44-4-4-24-40000-4400002-22-22-2200000000-22000000002-2−232323−23−232323−230000000000000000000000000000000000000000
χ7544-44-44-4-4-2-4400004-400002-22-22-22000000002-200000000-220000000023−23−232323−23−232300000000000000000000000000000000
χ7644-44-44-4-4-2-4400004-400002-22-22-22000000002-200000000-2200000000−232323−23−232323−2300000000000000000000000000000000
χ7744-4-44-44-4-2004-400004-400-2-222-222−2i2−2i22i22i2−2i2−2i22i22i200-2-222000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200000000000000000000000000000000
χ7844-4-44-44-4-2004-400004-400-2-222-2222i22i2−2i2−2i22i22i2−2i2−2i200-2-222000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200000000000000000000000000000000
χ7944-4-44-44-4-200-440000-4400-2-222-222−2i2−2i22i22i22i22i2−2i2−2i20022-2-2000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200000000000000000000000000000000
χ8044-4-44-44-4-200-440000-4400-2-222-2222i22i2−2i2−2i2−2i2−2i22i22i20022-2-2000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200000000000000000000000000000000
χ814-4444-4-4-44004-40000-4400-4-4444-4-400000000004-4-44000000000000000000000000000000000000000000000000000000
χ824-4444-4-4-4400-4400004-400-4-4444-4-40000000000-444-4000000000000000000000000000000000000000000000000000000
χ834-4444-4-4-4-2004-40000-440022-2-2-2220000000000-222-20000006−66−6−66−666−66−6−66−6600000000000000000000000000000000
χ844-4444-4-4-4-2004-40000-440022-2-2-2220000000000-222-2000000−66−666−66−6−66−666−66−600000000000000000000000000000000
χ854-4444-4-4-4-200-4400004-40022-2-2-22200000000002-2-220000006−66−6−66−66−66−666−66−600000000000000000000000000000000
χ864-4444-4-4-4-200-4400004-40022-2-2-22200000000002-2-22000000−66−666−66−66−66−6−66−6600000000000000000000000000000000
χ874-44-4-444-4-24-400004-40000-22-222-2200004i−4i4i−4i-2200000000-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ884-44-4-444-4-24-400004-40000-22-222-220000−4i4i−4i4i-2200000000-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ894-44-4-444-4-2-440000-440000-22-222-224i−4i4i−4i00002-2000000002-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ904-44-4-444-4-2-440000-440000-22-222-22−4i4i−4i4i00002-2000000002-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ914-4-44-4-444-200004-400004-4-222-222-222−22−222222−22−2222000000-2-22200−2−22222−2−2−2−22222−2−200000000000000000000000000000000
χ924-4-44-4-444-200004-400004-4-222-222-2−222222−22−222222−22000000-2-2220022−2−2−2−22222−2−2−2−22200000000000000000000000000000000
χ934-4-44-4-444-20000-440000-44-222-222-222−22−2222−222222−2200000022-2-200−2−22222−2−222−2−2−2−22200000000000000000000000000000000
χ944-4-44-4-444-20000-440000-44-222-222-2−222222−2222−22−222200000022-2-20022−2−2−2−222−2−22222−2−200000000000000000000000000000000
χ954-4-4-444-44-2444444-4-4-4-4-4-42222-2-2-200000000-2-2-22-22-22-2222000000000000000000000000000000000000000000000000
χ964-4-4-444-44-244-4-4-4-4-4-444442222-2-2-200000000-2-22-22-22-22-222000000000000000000000000000000000000000000000000

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