Finite Group Databasebeta

← Group #10698025

Character table — Group #10698025

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122222223444444444444666666688888888121212121212121212121212242424242424242424242424242424248888888888888888444412121212121212124444
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
χ922222222222-2-2-2-222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1022222222222-2-2-2-222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ11222222222-2-222-2-2-2-222-2-22222222000000002222-2-2-2-2-2-2-2-20000000000000000000000002222-2-2-2-20000000000000000
χ12222222222-2-222-2-2-2-222-2-22222222000000002222-2-2-2-2-2-2-2-2000000000000000000000000-2-2-2-222220000000000000000
χ13222222222-2-2-2-222-2-2-2-222222222200000000-2-2-2-22222-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000
χ14222222222-2-2-2-222-2-2-2-222222222200000000-2-2-2-22222-2-2-2-20000000000000000-2-2-2-22222000000000000000000000000
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
χ1922222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000−i3−i3i3i3−i3−i3i3i30000
χ2022222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000i3i3−i3−i3i3i3−i3−i30000
χ2122222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-100000000000000000000−i3−i3i3i3i3i3−i3−i30000
χ2222222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-100000000000000000000i3i3−i3−i3−i3−i3i3i30000
χ2322-2-222-2-222-200002-200002-2-2-2-222000022-2-2000000002-22-2000000002222-2-2-2-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ2422-2-222-2-222-200002-200002-2-2-2-222000022-2-2000000002-22-2000000002222-2-2-2-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ2522-2-222-2-222-200002-200002-2-2-2-2220000-2-222000000002-22-200000000-2-2-2-22222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ2622-2-222-2-222-200002-200002-2-2-2-2220000-2-222000000002-22-200000000-2-2-2-22222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ2722-2-222-2-22-220000-2200002-2-2-2-22222-2-2000000000000-22-222222-2-2-2-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2822-2-222-2-22-220000-2200002-2-2-2-22222-2-2000000000000-22-222222-2-2-2-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ2922-2-222-2-22-220000-2200002-2-2-2-222-2-222000000000000-22-22-2-2-2-2222200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ3022-2-222-2-22-220000-2200002-2-2-2-222-2-222000000000000-22-22-2-2-2-2222200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ312-22-22-22-2200002-200002-2-22-22-22-2−i2i2−i2i2−i2i2−i2i2000022-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002-22-2−i2i2−i2i2−i2i2−i2i20000000000000000
χ322-22-22-22-2200002-200002-2-22-22-22-2−i2i2−i2i2−i2i2−i2i2000022-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000-22-22i2−i2i2−i2i2−i2i2−i20000000000000000
χ332-22-22-22-2200002-200002-2-22-22-22-2i2−i2i2−i2i2−i2i2−i2000022-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002-22-2i2−i2i2−i2i2−i2i2−i20000000000000000
χ342-22-22-22-2200002-200002-2-22-22-22-2i2−i2i2−i2i2−i2i2−i2000022-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000-22-22−i2i2−i2i2−i2i2−i2i20000000000000000
χ352-22-22-22-220000-220000-22-22-22-22-2−i2i2−i2i2i2−i2i2−i20000-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22-22-20000−i2i2−i2i2i2−i2i2−i20000000000000000
χ362-22-22-22-220000-220000-22-22-22-22-2−i2i2−i2i2i2−i2i2−i20000-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-22-220000i2−i2i2−i2−i2i2−i2i20000000000000000
χ372-22-22-22-220000-220000-22-22-22-22-2i2−i2i2−i2−i2i2−i2i20000-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22-22-20000i2−i2i2−i2−i2i2−i2i20000000000000000
χ382-22-22-22-220000-220000-22-22-22-22-2i2−i2i2−i2−i2i2−i2i20000-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-22-220000−i2i2−i2i2i2−i2i2−i20000000000000000
χ392-2-222-2-222002-200002-200-2-22-222-2−i2i2i2−i2−i2i2i2−i222-2-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2−i2i2i2−i20000-222-20000000000000000
χ402-2-222-2-222002-200002-200-2-22-222-2−i2i2i2−i2−i2i2i2−i222-2-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2i2−i2−i2i200002-2-220000000000000000
χ412-2-222-2-222002-200002-200-2-22-222-2i2−i2−i2i2i2−i2−i2i222-2-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2−i2i2i2−i200002-2-220000000000000000
χ422-2-222-2-222002-200002-200-2-22-222-2i2−i2−i2i2i2−i2−i2i222-2-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2i2−i2−i2i20000-222-20000000000000000
χ432-2-222-2-22200-220000-2200-2-22-222-2−i2i2i2−i2i2−i2−i2i2-2-22200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2i2−i2−i2i2-222-200000000000000000000
χ442-2-222-2-22200-220000-2200-2-22-222-2−i2i2i2−i2i2−i2−i2i2-2-22200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2−i2i2i2−i22-2-2200000000000000000000
χ452-2-222-2-22200-220000-2200-2-22-222-2i2−i2−i2i2−i2i2i2−i2-2-22200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2i2−i2−i2i22-2-2200000000000000000000
χ462-2-222-2-22200-220000-2200-2-22-222-2i2−i2−i2i2−i2i2i2−i2-2-22200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2−i2i2i2−i2-222-200000000000000000000
χ472-2-2-2-22222222222-2-2-2-2-2-2-2-2-222-22000000002-22-22-22-222-2-2000000000000000000000000000000002i−2i002i−2i2i−2i00000000
χ482-2-2-2-22222222222-2-2-2-2-2-2-2-2-222-22000000002-22-22-22-222-2-200000000000000000000000000000000−2i2i00−2i2i−2i2i00000000
χ492-2-2-2-2222222-2-2-2-2-2-22222-2-2-222-2200000000-22-22-22-2222-2-200000000000000000000000000000000002-200002-22-20000
χ502-2-2-2-2222222-2-2-2-2-2-22222-2-2-222-2200000000-22-22-22-2222-2-20000000000000000000000000000000000-220000-22-220000
χ512-2-2-2-22222-2-222-2-222-2-222-2-2-222-22000000002-22-2-22-22-2-22200000000000000000000000000000000000000000000002-2
χ522-2-2-2-22222-2-222-2-222-2-222-2-2-222-22000000002-22-2-22-22-2-2220000000000000000000000000000000000000000000000-22
χ532-2-2-2-22222-2-2-2-2222222-2-2-2-2-222-2200000000-22-222-22-2-2-222000000000000000000000000000000000000000000002-200
χ542-2-2-2-22222-2-2-2-2222222-2-2-2-2-222-2200000000-22-222-22-2-2-22200000000000000000000000000000000000000000000-2200
χ552-2-2-2-2222-1222222-2-2-2-2-2-2111-1-11-100000000-11-11-11-11-1-1113−33−33−33−33−33−33−33−300000000000000002i−2i00−ii−ii−i3i3i3−i30000
χ562-2-2-2-2222-1222222-2-2-2-2-2-2111-1-11-100000000-11-11-11-11-1-1113−33−33−33−33−33−33−33−30000000000000000−2i2i00i−ii−ii3−i3−i3i30000
χ572-2-2-2-2222-1222222-2-2-2-2-2-2111-1-11-100000000-11-11-11-11-1-111−33−33−33−33−33−33−33−3300000000000000002i−2i00−ii−iii3−i3−i3i30000
χ582-2-2-2-2222-1222222-2-2-2-2-2-2111-1-11-100000000-11-11-11-11-1-111−33−33−33−33−33−33−33−330000000000000000−2i2i00i−ii−i−i3i3i3−i30000
χ592-2-2-2-2222-122-2-2-2-2-2-22222111-1-11-1000000001-11-11-11-1-1-1113−33−33−33−3−33−33−33−330000000000000000002-23−3−33-11-110000
χ602-2-2-2-2222-122-2-2-2-2-2-22222111-1-11-1000000001-11-11-11-1-1-1113−33−33−33−3−33−33−33−33000000000000000000-22−333−31-11-10000
χ612-2-2-2-2222-122-2-2-2-2-2-22222111-1-11-1000000001-11-11-11-1-1-111−33−33−33−333−33−33−33−30000000000000000002-2−333−3-11-110000
χ622-2-2-2-2222-122-2-2-2-2-2-22222111-1-11-1000000001-11-11-11-1-1-111−33−33−33−333−33−33−33−3000000000000000000-223−3−331-11-10000
χ6344444444-2-4-444-4-4-4-444-4-4-2-2-2-2-2-2-200000000-2-2-2-222222222000000000000000000000000000000000000000000000000
χ6444444444-2-4-4-4-444-4-4-4-444-2-2-2-2-2-2-2000000002222-2-2-2-22222000000000000000000000000000000000000000000000000
χ65444-4-4-4-444004-40000-440044-4-44-4-4000000004-4-4400000000000000000000000000000000000000000000000000000000
χ66444-4-4-4-44400-4400004-40044-4-44-4-400000000-444-400000000000000000000000000000000000000000000000000000000
χ67444-4-4-4-44-2004-40000-4400-2-222-22200000000-222-200000000i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000
χ68444-4-4-4-44-2004-40000-4400-2-222-22200000000-222-200000000−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000
χ69444-4-4-4-44-200-4400004-400-2-222-222000000002-2-2200000000i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000
χ70444-4-4-4-44-200-4400004-400-2-222-222000000002-2-2200000000−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000
χ7144-44-4-44-4400004-40000-444-444-4-4-40000000000004-4-440000000000000000000000000000000000000000000000000000
χ7244-44-4-44-440000-4400004-44-444-4-4-4000000000000-444-40000000000000000000000000000000000000000000000000000
χ7344-44-4-44-4-200004-40000-44-22-2-2222000000000000-222-20000i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000
χ7444-44-4-44-4-200004-40000-44-22-2-2222000000000000-222-20000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000
χ7544-44-4-44-4-20000-4400004-4-22-2-22220000000000002-2-220000i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000
χ7644-44-4-44-4-20000-4400004-4-22-2-22220000000000002-2-220000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000
χ7744-4-444-4-4-24-400004-40000-22222-2-2000044-4-400000000-22-2200000000-2-2-2-2222200000000000000000000000000000000
χ7844-4-444-4-4-24-400004-40000-22222-2-20000-4-44400000000-22-22000000002222-2-2-2-200000000000000000000000000000000
χ7944-4-444-4-4-2-440000-440000-22222-2-244-4-40000000000002-22-2-2-2-2-222220000000000000000000000000000000000000000
χ8044-4-444-4-4-2-440000-440000-22222-2-2-4-4440000000000002-22-22222-2-2-2-20000000000000000000000000000000000000000
χ814-444-44-4-444-40000-440000-444-4-4-4400000000000000004-4-44000000000000000000000000000000000000000000000000
χ824-444-44-4-44-4400004-40000-444-4-4-440000000000000000-444-4000000000000000000000000000000000000000000000000
χ834-444-44-4-4-24-40000-4400002-2-2222-20000000000000000-222-20000000023−2323−23−2323−232300000000000000000000000000000000
χ844-444-44-4-4-24-40000-4400002-2-2222-20000000000000000-222-200000000−2323−232323−2323−2300000000000000000000000000000000
χ854-444-44-4-4-2-4400004-400002-2-2222-200000000000000002-2-2223−2323−23−2323−23230000000000000000000000000000000000000000
χ864-444-44-4-4-2-4400004-400002-2-2222-200000000000000002-2-22−2323−232323−2323−230000000000000000000000000000000000000000
χ874-44-44-44-4-200004-400004-42-22-22-22−2i22i2−2i22i2−2i22i2−2i22i20000-2-2220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ884-44-44-44-4-200004-400004-42-22-22-222i2−2i22i2−2i22i2−2i22i2−2i20000-2-2220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ894-44-44-44-4-20000-440000-442-22-22-22−2i22i2−2i22i22i2−2i22i2−2i2000022-2-20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ904-44-44-44-4-20000-440000-442-22-22-222i2−2i22i2−2i2−2i22i2−2i22i2000022-2-20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ914-4-444-4-44-2004-400004-40022-22-2-22−2i22i22i2−2i2−2i22i22i2−2i2-2-22200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ924-4-444-4-44-2004-400004-40022-22-2-222i2−2i2−2i22i22i2−2i2−2i22i2-2-22200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ934-4-444-4-44-200-440000-440022-22-2-22−2i22i22i2−2i22i2−2i2−2i22i222-2-200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ944-4-444-4-44-200-440000-440022-22-2-222i2−2i2−2i22i2−2i22i22i2−2i222-2-200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ954-4-4-4-4444-2-4-444-4-444-4-444222-2-22-200000000-22-222-22-222-2-2000000000000000000000000000000000000000000000000
χ964-4-4-4-4444-2-4-4-4-4444444-4-4222-2-22-2000000002-22-2-22-2222-2-2000000000000000000000000000000000000000000000000

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