Finite Group Databasebeta

← Group #10694701

Character table — Group #10694701

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12222222223444466666668888888844666688881212121212121212242424242424242424242424242424244444444488888888444412121212121212124444
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
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-11-11
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111-11-1
χ9111111-1-1-1-1111-1-111-1-11-1-11111-1-1-1-11-111-1-111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i11-1-1
χ10111111-1-1-1-1111-1-111-1-11-1-11111-1-1-1-11-111-1-111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-1-111
χ11111111-1-1-1-1111-1-111-1-11-1-11111-1-1-1-11-111-1-111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i-1-111
χ12111111-1-1-1-1111-1-111-1-11-1-11111-1-1-1-11-111-1-111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii11-1-1
χ13111111-1-1-1-1111-1-111-1-11-1-1-1-1-1-111111-111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii1-1-11
χ14111111-1-1-1-1111-1-111-1-11-1-1-1-1-1-111111-111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-111-1
χ15111111-1-1-1-1111-1-111-1-11-1-1-1-1-1-111111-111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-111-1
χ16111111-1-1-1-1111-1-111-1-11-1-1-1-1-1-111111-111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i1-1-11
χ1722222222222-2-2-2-2222222200000000-2-222220000-2-2-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ1822222222222-2-2-2-2222222200000000-2-222220000-2-2-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ192222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ202222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ212222222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ222222222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ23222222-2-2-2-22-2-22222-2-22-2-200000000-2222-2-20000-2-2-22222-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ24222222-2-2-2-22-2-22222-2-22-2-200000000-2222-2-20000-2-2-22222-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ25222222-2-2-2-2-122-2-2-1-111-1112222-2-2-2-22-2-1-11122-2-2-1-1-11111-1-1-1-1-1-1-1-1-11111111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ26222222-2-2-2-2-122-2-2-1-111-1112222-2-2-2-22-2-1-11122-2-2-1-1-11111-1-1-1-1-1-1-1-1-1111111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ27222222-2-2-2-2-122-2-2-1-111-111-2-2-2-222222-2-1-111-2-222-1-1-11111-111111111-1-1-1-1-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ28222222-2-2-2-2-122-2-2-1-111-111-2-2-2-222222-2-1-111-2-222-1-1-11111-111111111-1-1-1-1-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ292222-2-22-2-22222-2-222222222222-2-2-2-2-22-2-2-2-2-2-2222-2-222-2-222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ302222-2-22-2-22222-2-22222222-2-2-2-22222-22-2-2-2-222-2-22-2-222-2-22-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ312222-2-22-2-222-2-2222222222000000002-2-2-2-2-20000-222-2-222-200000000000000000000000022-2-222-2-20000000000000000
χ322222-2-22-2-222-2-2222222222000000002-2-2-2-2-20000-222-2-222-2000000000000000000000000-2-222-2-2220000000000000000
χ332222-2-22-2-22-122-2-2-1-1-1-1-1-1-12222-2-2-2-2-221111-2-222-111-1-111-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ342222-2-22-2-22-122-2-2-1-1-1-1-1-1-12222-2-2-2-2-221111-2-222-111-1-111-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ352222-2-22-2-22-122-2-2-1-1-1-1-1-1-1-2-2-2-22222-22111122-2-2-111-1-111-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ362222-2-22-2-22-122-2-2-1-1-1-1-1-1-1-2-2-2-22222-22111122-2-2-111-1-111-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ372222-2-2-222-22222222-2-22-2-222222222-2-2-2-222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ382222-2-2-222-22222222-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ392222-2-2-222-22-2-2-2-222-2-22-2-20000000022-2-2220000-22222-2-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-2-222-22-2-2-2-222-2-22-2-20000000022-2-2220000-22222-2-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412222-2-2-222-2-12222-1-111-11122222222-2-211-1-1-2-2-2-2-11111-1-1-1-1-1-1-111111111-1-1-1-1000000000000000000003−3−333−3−330000
χ422222-2-2-222-2-12222-1-111-11122222222-2-211-1-1-2-2-2-2-11111-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000−333−3−333−30000
χ432222-2-2-222-2-12222-1-111-111-2-2-2-2-2-2-2-2-2-211-1-12222-11111-1-1-11111-1-1-1-1-1-1-1-11111000000000000000000003−3−33−333−30000
χ442222-2-2-222-2-12222-1-111-111-2-2-2-2-2-2-2-2-2-211-1-12222-11111-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−333−33−3−330000
χ4522-2-22-222-2-2200002-222-2-2-222−2−222−2−2002-22-22−22−20000000022−2−222−2−222−2−222−2−2002-2002-22−22−22−22−20000000000000000
χ4622-2-22-222-2-2200002-222-2-2-222−2−222−2−2002-22-22−22−20000000022−2−222−2−222−2−222−2−200-2200-22−22−22−22−220000000000000000
χ4722-2-22-222-2-2200002-222-2-2-2−2−222−2−222002-22-2−22−2200000000−2−222−2−222−2−222−2−222002-2002-2−22−22−22−220000000000000000
χ4822-2-22-222-2-2200002-222-2-2-2−2−222−2−222002-22-2−22−2200000000−2−222−2−222−2−222−2−22200-2200-222−22−22−22−20000000000000000
χ4922-2-22-2-2-222200002-2-2-2-22222−2−2−2−222002-2-222−2−220000000022−2−222−2−2−2−222−2−222002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ5022-2-22-2-2-222200002-2-2-2-22222−2−2−2−222002-2-222−2−220000000022−2−222−2−2−2−222−2−22200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ5122-2-22-2-2-222200002-2-2-2-222−2−22222−2−2002-2-22−222−200000000−2−222−2−22222−2−222−2−2002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ5222-2-22-2-2-222200002-2-2-2-222−2−22222−2−2002-2-22−222−200000000−2−222−2−22222−2−222−2−200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ5322-2-2-222-22-2200002-222-2-2-222−2−2−2−22200-22-22−222−20000000022−2−2−2−22222−2−2−2−2222-2002-2002−2−222−2−220000000000000000
χ5422-2-2-222-22-2200002-222-2-2-222−2−2−2−22200-22-22−222−20000000022−2−2−2−22222−2−2−2−222-2200-2200−222−2−222−20000000000000000
χ5522-2-2-222-22-2200002-222-2-2-2−2−22222−2−200-22-222−2−2200000000−2−22222−2−2−2−22222−2−22-2002-200−222−2−222−20000000000000000
χ5622-2-2-222-22-2200002-222-2-2-2−2−22222−2−200-22-222−2−2200000000−2−22222−2−2−2−22222−2−2-2200-22002−2−222−2−220000000000000000
χ5722-2-2-22-22-22200002-2-2-2-22222−2−222−2−200-222-2−22−220000000022−2−2−2−222−2−22222−2−22i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ5822-2-2-22-22-22200002-2-2-2-22222−2−222−2−200-222-2−22−220000000022−2−2−2−222−2−22222−2−2−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ5922-2-2-22-22-22200002-2-2-2-222−2−222−2−22200-222-22−22−200000000−2−22222−2−222−2−2−2−2222i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ6022-2-2-22-22-22200002-2-2-2-222−2−222−2−22200-222-22−22−200000000−2−22222−2−222−2−2−2−222−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ614444444444-2-4-4-4-4-2-2-2-2-2-2-200000000-4-4-2-2-2-2000022222222000000000000000000000000000000000000000000000000
χ62444444-4-4-4-4-2-4-444-2-222-22200000000-44-2-2220000222-2-2-2-22000000000000000000000000000000000000000000000000
χ634444-4-44-4-44-2-4-444-2-2-2-2-2-2-2000000004-4222200002-2-222-2-22000000000000000000000000000000000000000000000000
χ644444-4-4-444-4-2-4-4-4-4-2-222-222000000004422-2-200002-2-2-2-2222000000000000000000000000000000000000000000000000
χ6544-4-44-444-4-4-20000-22-2-22222222−22−222222−22−2200-22-2222−2222−2200000000−2−222−2−222−2−222−2−22200000000000000000000000000000000
χ6644-4-44-444-4-4-20000-22-2-2222−22−222222−22−22222200-22-22−2222−22220000000022−2−222−2−222−2−222−2−200000000000000000000000000000000
χ6744-4-44-4-4-444-20000-22222-2-22222−22−22−22−22222200-222-222−22−222200000000−2−222−2−22222−2−222−2−200000000000000000000000000000000
χ6844-4-44-4-4-444-20000-22222-2-2−22−2222222222−22−2200-222-2−222222−220000000022−2−222−2−2−2−222−2−22200000000000000000000000000000000
χ6944-4-4-444-44-4-20000-22-2-22222222−22−22−22−222222002-22-2−222222−2200000000−2−22222−2−2−2−22222−2−200000000000000000000000000000000
χ7044-4-4-444-44-4-20000-22-2-2222−22−2222222222−22−22002-22-222−22−22220000000022−2−2−2−22222−2−2−2−22200000000000000000000000000000000
χ7144-4-4-44-44-44-20000-22222-2-22222−22−222222−22−22002-2-22−2222−222200000000−2−22222−2−222−2−2−2−22200000000000000000000000000000000
χ7244-4-4-44-44-44-20000-22222-2-2−22−222222−22−222222002-2-2222−2222−220000000022−2−2−2−222−2−22222−2−200000000000000000000000000000000
χ734-44-40000004004i−4i-4400-40022−2222−22−2i22i2−2i22i20000000000000004i−4i022−2222−2200000000−2i22i2−2i22i200000000000000000000000000000000
χ744-44-40000004004i−4i-4400-400−2222−22222i2−2i22i2−2i20000000000000004i−4i0−2222−2222000000002i2−2i22i2−2i200000000000000000000000000000000
χ754-44-4000000400−4i4i-4400-40022−2222−222i2−2i22i2−2i2000000000000000−4i4i022−2222−22000000002i2−2i22i2−2i200000000000000000000000000000000
χ764-44-4000000400−4i4i-4400-400−2222−2222−2i22i2−2i22i2000000000000000−4i4i0−2222−222200000000−2i22i2−2i22i200000000000000000000000000000000
χ774-44-4000000-2004i−4i2-2−2i32i32−2i32i322−2222−22−2i22i2−2i22i20000000000023−2300−2i2i0−22−226−66−6i6−i6i6−i6i2−i2i2−i200000000000000000000000000000000
χ784-44-4000000-2004i−4i2-2−2i32i32−2i32i3−2222−22222i2−2i22i2−2i20000000000023−2300−2i2i02−22−2−66−66−i6i6−i6i6−i2i2−i2i200000000000000000000000000000000
χ794-44-4000000-2004i−4i2-22i3−2i322i3−2i322−2222−22−2i22i2−2i22i200000000000−232300−2i2i0−22−22−66−66−i6i6−i6i6i2−i2i2−i200000000000000000000000000000000
χ804-44-4000000-2004i−4i2-22i3−2i322i3−2i3−2222−22222i2−2i22i2−2i200000000000−232300−2i2i02−22−26−66−6i6−i6i6−i6−i2i2−i2i200000000000000000000000000000000
χ814-44-4000000-200−4i4i2-2−2i32i32−2i32i322−2222−222i2−2i22i2−2i200000000000−2323002i−2i0−22−22−66−66i6−i6i6−i6−i2i2−i2i200000000000000000000000000000000
χ824-44-4000000-200−4i4i2-2−2i32i32−2i32i3−2222−2222−2i22i2−2i22i200000000000−2323002i−2i02−22−26−66−6−i6i6−i6i6i2−i2i2−i200000000000000000000000000000000
χ834-44-4000000-200−4i4i2-22i3−2i322i3−2i322−2222−222i2−2i22i2−2i20000000000023−23002i−2i0−22−226−66−6−i6i6−i6i6−i2i2−i2i200000000000000000000000000000000
χ844-44-4000000-200−4i4i2-22i3−2i322i3−2i3−2222−2222−2i22i2−2i22i20000000000023−23002i−2i02−22−2−66−66i6−i6i6−i6i2−i2i2−i200000000000000000000000000000000
χ854-4-4400000044-400-4-40040000004i−4i−4i4i00000000004000000-40000000000004i−4i−4i4i00000000000000000000000000000000
χ864-4-4400000044-400-4-4004000000−4i4i4i−4i00000000004000000-4000000000000−4i4i4i−4i00000000000000000000000000000000
χ874-4-440000004-4400-4-4004004-4-4400000000000000-400000044-4-4400000000000000000000000000000000000000000000
χ884-4-440000004-4400-4-400400-444-400000000000000-40000004-444-400000000000000000000000000000000000000000000
χ894-4-44000000-24-40022−2i32i3-22i3−2i300004i−4i−4i4i0000000000-200−2i32i30020000−232323−230000−2i2i2i−2i00000000000000000000000000000000
χ904-4-44000000-24-40022−2i32i3-22i3−2i30000−4i4i4i−4i0000000000-200−2i32i3002000023−23−232300002i−2i−2i2i00000000000000000000000000000000
χ914-4-44000000-24-400222i3−2i3-2−2i32i300004i−4i−4i4i0000000000-2002i3−2i3002000023−23−23230000−2i2i2i−2i00000000000000000000000000000000
χ924-4-44000000-24-400222i3−2i3-2−2i32i30000−4i4i4i−4i0000000000-2002i3−2i30020000−232323−2300002i−2i−2i2i00000000000000000000000000000000
χ934-4-44000000-2-440022−2i32i3-22i3−2i34-4-44000000000000002002i3−2i300-2-222-200002i3−2i3−2i32i3000000000000000000000000000000000000
χ944-4-44000000-2-440022−2i32i3-22i3−2i3-444-4000000000000002002i3−2i300-22-2-220000−2i32i32i3−2i3000000000000000000000000000000000000
χ954-4-44000000-2-4400222i3−2i3-2−2i32i34-4-4400000000000000200−2i32i300-2-222-20000−2i32i32i3−2i3000000000000000000000000000000000000
χ964-4-44000000-2-4400222i3−2i3-2−2i32i3-444-400000000000000200−2i32i300-22-2-2200002i3−2i3−2i32i3000000000000000000000000000000000000

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