Finite Group Databasebeta

← Group #10694967

Character table — Group #10694967

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122222223444444444444666666688888888121212121212121212121212242424242424242424242424242424248888888888888888444412121212121212122244
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
χ91-1-111-11-1111-1-111-1-111-1-1-1-1-111-11iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-1i−i1-1ii−i−i11-1-11-1i−i
χ101-1-111-11-1111-1-111-1-111-1-1-1-1-111-11iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−ii-11−i−iii-1-111-11−ii
χ111-1-111-11-1111-1-111-1-111-1-1-1-1-111-11iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-11111i−i1-1ii−i−i11-1-1-11−ii
χ121-1-111-11-1111-1-111-1-111-1-1-1-1-111-11iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-11111−ii-11−i−iii-1-1111-1i−i
χ131-1-111-11-1111-1-111-1-111-1-1-1-1-111-11−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-11111i−i-11ii−i−i-1-1111-1−ii
χ141-1-111-11-1111-1-111-1-111-1-1-1-1-111-11−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-11111−ii1-1−i−iii11-1-1-11i−i
χ151-1-111-11-1111-1-111-1-111-1-1-1-1-111-11−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-1i−i-11ii−i−i-1-111-11i−i
χ161-1-111-11-1111-1-111-1-111-1-1-1-1-111-11−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-1−ii1-1−i−iii11-1-11-1−ii
χ1722222222222-2-2-2-222-2-2-2-2222222222-2-222-2-222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ1822222222222-2-2-2-222-2-2-2-22222222-2-222-2-22222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ19222222222-2-222-2-2-2-222-2-2222222200000000-2-22222-2-2-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ20222222222-2-222-2-2-2-222-2-2222222200000000-2-22222-2-2-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ21222222222-2-2-2-222-2-2-2-222222222200000000-2-2-2-2-2-22222-2-2000000000000000022-2-222-2-2000000000000000000000000
χ22222222222-2-2-2-222-2-2-2-222222222200000000-2-2-2-2-2-22222-2-20000000000000000-2-222-2-222000000000000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2422222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2522222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ2622222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ2722222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2-1-111111111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2822222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2-1-111111111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2922222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-2-222-2-222-1-111111111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ3022222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-2-222-2-222-1-111111111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ3122-22-22-2-222-200002-200002-2-22-22-2002i−2i002i−2i2-2000000002-200002i2i−2i−2i00002i2i−2i−2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ3222-22-22-2-222-200002-200002-2-22-22-2002i−2i002i−2i2-2000000002-200002i2i−2i−2i00002i2i−2i−2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ3322-22-22-2-222-200002-200002-2-22-22-200−2i2i00−2i2i2-2000000002-20000−2i−2i2i2i0000−2i−2i2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3422-22-22-2-222-200002-200002-2-22-22-200−2i2i00−2i2i2-2000000002-20000−2i−2i2i2i0000−2i−2i2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ3522-22-22-2-22-220000-2200002-2-22-22-22i−2i002i−2i00-2200000000-222i2i−2i−2i00002i2i−2i−2i00002−2−222−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ3622-22-22-2-22-220000-2200002-2-22-22-22i−2i002i−2i00-2200000000-222i2i−2i−2i00002i2i−2i−2i0000−222−2−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ3722-22-22-2-22-220000-2200002-2-22-22-2−2i2i00−2i2i00-2200000000-22−2i−2i2i2i0000−2i−2i2i2i00002−2−222−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ3822-22-22-2-22-220000-2200002-2-22-22-2−2i2i00−2i2i00-2200000000-22−2i−2i2i2i0000−2i−2i2i2i0000−222−2−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ392-222-2-2-2222-20000-220000-2222-2-2-2002-200-222-200000000-22000022-2-20000-2-222−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ402-222-2-2-2222-20000-220000-2222-2-2-2002-200-222-200000000-22000022-2-20000-2-222i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ412-222-2-2-2222-20000-220000-2222-2-2-200-22002-22-200000000-220000-2-222000022-2-2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ422-222-2-2-2222-20000-220000-2222-2-2-200-22002-22-200000000-220000-2-222000022-2-2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ432-222-2-2-222-2200002-20000-2222-2-2-22-200-2200-22000000002-222-2-20000-2-2220000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ442-222-2-2-222-2200002-20000-2222-2-2-22-200-2200-22000000002-222-2-20000-2-2220000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ452-222-2-2-222-2200002-20000-2222-2-2-2-22002-200-22000000002-2-2-222000022-2-20000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ462-222-2-2-222-2200002-20000-2222-2-2-2-22002-200-22000000002-2-2-222000022-2-20000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ472-2-222-22-222222-2-2-2-2-2-222-2-2-222-222i2i−2i−2i−2i−2i2i2i22-2-222-2-222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ482-2-222-22-222222-2-2-2-2-2-222-2-2-222-22−2i−2i2i2i2i2i−2i−2i22-2-222-2-222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ492-2-222-22-22-2-2222222-2-2-2-2-2-2-222-2200000000-2-2-2-22222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ502-2-222-22-22-2-2222222-2-2-2-2-2-2-222-2200000000-2-2-2-22222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ512-2-222-22-22-2-2-2-2-2-2222222-2-2-222-2200000000-2-222-2-2-2-2222200000000000000000000000022-2-2-2-2220000000000000000
χ522-2-222-22-22-2-2-2-2-2-2222222-2-2-222-2200000000-2-222-2-2-2-22222000000000000000000000000-2-22222-2-20000000000000000
χ532-2-222-22-2-12222-2-2-2-2-2-222111-1-11-12i2i−2i−2i−2i−2i2i2i-1-111-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i000000000000000000003−3−33−i3i3i3−i30000
χ542-2-222-22-2-12222-2-2-2-2-2-222111-1-11-12i2i−2i−2i−2i−2i2i2i-1-111-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000−333−3i3−i3−i3i30000
χ552-2-222-22-2-12222-2-2-2-2-2-222111-1-11-1−2i−2i2i2i2i2i−2i−2i-1-111-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii000000000000000000003−3−33i3−i3−i3i30000
χ562-2-222-22-2-12222-2-2-2-2-2-222111-1-11-1−2i−2i2i2i2i2i−2i−2i-1-111-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii00000000000000000000−333−3−i3i3i3−i30000
χ572-2-222-22-2-122-2-222-2-222-2-2111-1-11-12i2i2i2i−2i−2i−2i−2i-1-1-1-111-1-11111−i−i−i−i−i−i−i−iiiiiiiii00000000000000002i−2i2-2−i−iii-1-1110000
χ582-2-222-22-2-122-2-222-2-222-2-2111-1-11-12i2i2i2i−2i−2i−2i−2i-1-1-1-111-1-11111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000−2i2i-22ii−i−i11-1-10000
χ592-2-222-22-2-122-2-222-2-222-2-2111-1-11-1−2i−2i−2i−2i2i2i2i2i-1-1-1-111-1-11111iiiiiiii−i−i−i−i−i−i−i−i00000000000000002i−2i-22−i−iii11-1-10000
χ602-2-222-22-2-122-2-222-2-222-2-2111-1-11-1−2i−2i−2i−2i2i2i2i2i-1-1-1-111-1-11111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000−2i2i2-2ii−i−i-1-1110000
χ6144444444-2-4-444-4-4-4-444-4-4-2-2-2-2-2-2-20000000022-2-2-2-2222222000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-444-4-4-4-444-2-2-2-2-2-2-200000000222222-2-2-2-222000000000000000000000000000000000000000000000000
χ63444-44-4-4-44004-400004-40044-4-44-4-400000000004-44-4000000000000000000000000000000000000000000000000000000
χ64444-44-4-4-4400-440000-440044-4-44-4-40000000000-44-44000000000000000000000000000000000000000000000000000000
χ65444-44-4-4-4-2004-400004-400-2-222-2220000000000-22-22000000i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i600000000000000000000000000000000
χ66444-44-4-4-4-2004-400004-400-2-222-2220000000000-22-22000000−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i600000000000000000000000000000000
χ67444-44-4-4-4-200-440000-4400-2-222-22200000000002-22-2000000i6−i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ68444-44-4-4-4-200-440000-4400-2-222-22200000000002-22-2000000−i6i6−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ6944-44-44-4-4-24-400004-40000-222-22-22004i−4i004i−4i-2200000000-220000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000000000000000
χ7044-44-44-4-4-24-400004-40000-222-22-2200−4i4i00−4i4i-2200000000-2200002i2i−2i−2i00002i2i−2i−2i00000000000000000000000000000000
χ7144-44-44-4-4-2-440000-440000-222-22-224i−4i004i−4i002-2000000002-2−2i−2i2i2i0000−2i−2i2i2i000000000000000000000000000000000000
χ7244-44-44-4-4-2-440000-440000-222-22-22−4i4i00−4i4i002-2000000002-22i2i−2i−2i00002i2i−2i−2i000000000000000000000000000000000000
χ7344-4-4-4-444400004-400004-44-44-4-4-44000000000000004-44-400000000000000000000000000000000000000000000000000
χ7444-4-4-4-44440000-440000-444-44-4-4-4400000000000000-44-4400000000000000000000000000000000000000000000000000
χ7544-4-4-4-444-200004-400004-4-22-2222-200000000000000-22-22006−6−66−666−66−6−66−666−600000000000000000000000000000000
χ7644-4-4-4-444-200004-400004-4-22-2222-200000000000000-22-2200−666−66−6−66−666−66−6−6600000000000000000000000000000000
χ7744-4-4-4-444-20000-440000-44-22-2222-2000000000000002-22-2006−6−666−6−666−6−666−6−6600000000000000000000000000000000
χ7844-4-4-4-444-20000-440000-44-22-2222-2000000000000002-22-200−666−6−666−6−666−6−666−600000000000000000000000000000000
χ794-444-4-4-44-24-40000-4400002-2-2-2222004-400-44-22000000002-20000-2-222000022-2-200000000000000000000000000000000
χ804-444-4-4-44-24-40000-4400002-2-2-222200-44004-4-22000000002-2000022-2-20000-2-22200000000000000000000000000000000
χ814-444-4-4-44-2-4400004-400002-2-2-22224-400-44002-200000000-22-2-222000022-2-2000000000000000000000000000000000000
χ824-444-4-4-44-2-4400004-400002-2-2-2222-44004-4002-200000000-2222-2-20000-2-222000000000000000000000000000000000000
χ834-44-4-444-4400004-40000-44-44-4-4-444000000000000004-4-4400000000000000000000000000000000000000000000000000
χ844-44-4-444-440000-4400004-4-44-4-4-44400000000000000-444-400000000000000000000000000000000000000000000000000
χ854-44-4-444-4-200004-40000-442-2222-2-200000000000000-222-200i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000
χ864-44-4-444-4-200004-40000-442-2222-2-200000000000000-222-200−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000
χ874-44-4-444-4-20000-4400004-42-2222-2-2000000000000002-2-2200i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000
χ884-44-4-444-4-20000-4400004-42-2222-2-2000000000000002-2-2200−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000
χ894-4-444-44-4-2-4-4444444-4-4-4-4222-2-22-2000000002222-2-2-2-222-2-2000000000000000000000000000000000000000000000000
χ904-4-444-44-4-2-4-4-4-4-4-4444444222-2-22-20000000022-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ914-4-4-444-444004-40000-4400-4-44-444-40000000000-444-4000000000000000000000000000000000000000000000000000000
χ924-4-4-444-44400-4400004-400-4-44-444-400000000004-4-44000000000000000000000000000000000000000000000000000000
χ934-4-4-444-44-2004-40000-440022-22-2-2200000000002-2-220000006−66−6−66−66−66−666−66−600000000000000000000000000000000
χ944-4-4-444-44-2004-40000-440022-22-2-2200000000002-2-22000000−66−666−66−66−66−6−66−6600000000000000000000000000000000
χ954-4-4-444-44-200-4400004-40022-22-2-220000000000-222-20000006−66−66−66−6−66−66−66−6600000000000000000000000000000000
χ964-4-4-444-44-200-4400004-40022-22-2-220000000000-222-2000000−66−66−66−666−66−66−66−600000000000000000000000000000000

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