Finite Group Databasebeta

← Group #10694586

Character table — Group #10694586

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12222234444444466688888888121212124466888812121212121212121212242424242424242424242424242424244444444488888888888824242424242424242444
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
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-11-1-111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i1-11-1
χ101111-1-11-1-111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-11-11
χ111111-1-11-1-111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i-11-11
χ121111-1-11-1-111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii1-11-1
χ131111-1-11-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii1-1-11
χ141111-1-11-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-111-1
χ151111-1-11-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-111-1
χ161111-1-11-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i1-1-11
χ17222222222-2-2-2-2-2-222200000000-2-2-2-22-222000022-2-222-2-2-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ18222222222-2-2-2-2-2-222200000000-2-2-2-22-222000022-2-222-2-2-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ192222222-2-222-2-22222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ202222222-2-222-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ212222222-2-2-2-222-2-2222000000002222-22220000-2-222-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ222222222-2-2-2-222-2-2222000000002222-22220000-2-222-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ23222222-122222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ24222222-122222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ25222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ26222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ27222222-1-2-222-2-222-1-1-1222222221111-2-2-1-1-2-2-2-2111111-1-1-1-1-1-1-1-11111-1-1-1-11111000000000000000000003−33−33−33−30000
χ28222222-1-2-222-2-222-1-1-1222222221111-2-2-1-1-2-2-2-2111111-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−33−33−33−330000
χ29222222-1-2-222-2-222-1-1-1-2-2-2-2-2-2-2-21111-2-2-1-12222111111-1-1-1-11111-1-1-1-11111-1-1-1-1000000000000000000003−33−3−33−330000
χ30222222-1-2-222-2-222-1-1-1-2-2-2-2-2-2-2-21111-2-2-1-12222111111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000−33−333−33−30000
χ312222-2-22222222-2-22222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ322222-2-22222222-2-2222-2-2-2-222222222-2-2-2-222-2-2-2-2-2-222-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ332222-2-2222-2-2-2-22222200000000-2-2-2-2-22-2-20000-2-2222222-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ342222-2-2222-2-2-2-22222200000000-2-2-2-2-22-2-20000-2-2222222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ352222-2-22-2-2-2-222222220000000022222-2-2-2000022-2-2-2-222-2-200000000000000000000000022-2-2-2-2220000000000000000
χ362222-2-22-2-2-2-222222220000000022222-2-2-2000022-2-2-2-222-2-2000000000000000000000000-2-22222-2-20000000000000000
χ372222-2-2-1222222-2-2-1-1-12222-2-2-2-2-1-1-1-1-2-211-2-2221111-1-111-1-1-1-1-1-111111111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ382222-2-2-1222222-2-2-1-1-12222-2-2-2-2-1-1-1-1-2-211-2-2221111-1-111-1-1-1-1-1-111111111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ392222-2-2-1222222-2-2-1-1-1-2-2-2-22222-1-1-1-1-2-21122-2-21111-1-111-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ402222-2-2-1222222-2-2-1-1-1-2-2-2-22222-1-1-1-1-2-21122-2-21111-1-111-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ412222-2-2-1-2-222-2-2-2-2-1-1-12222-2-2-2-21111221122-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ422222-2-2-1-2-222-2-2-2-2-1-1-12222-2-2-2-21111221122-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ432222-2-2-1-2-222-2-2-2-2-1-1-1-2-2-2-2222211112211-2-222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ442222-2-2-1-2-222-2-2-2-2-1-1-1-2-2-2-2222211112211-2-222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ4522-2-20022i−2i2-22i−2i002-2-2000022-2-22i2i−2i−2i00002i−2i0000002i−2i002-200002i2i−2i−2i22-2-200001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4622-2-20022i−2i2-22i−2i002-2-2000022-2-22i2i−2i−2i00002i−2i0000002i−2i002-200002i2i−2i−2i22-2-20000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4722-2-20022i−2i2-22i−2i002-2-20000-2-2222i2i−2i−2i0000−2i2i0000002i−2i002-20000−2i−2i2i2i-2-22200001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4822-2-20022i−2i2-22i−2i002-2-20000-2-2222i2i−2i−2i0000−2i2i0000002i−2i002-20000−2i−2i2i2i-2-2220000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4922-2-20022i−2i-22−2i2i002-2-22i2i−2i−2i0000−2i−2i2i2i0000002-200002i−2i00-222i2i−2i−2i0000000022-2-21−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ5022-2-20022i−2i-22−2i2i002-2-22i2i−2i−2i0000−2i−2i2i2i0000002-200002i−2i00-222i2i−2i−2i0000000022-2-2−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ5122-2-20022i−2i-22−2i2i002-2-2−2i−2i2i2i0000−2i−2i2i2i000000-2200002i−2i00-22−2i−2i2i2i00000000-2-2221−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ5222-2-20022i−2i-22−2i2i002-2-2−2i−2i2i2i0000−2i−2i2i2i000000-2200002i−2i00-22−2i−2i2i2i00000000-2-222−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ5322-2-2002−2i2i2-2−2i2i002-2-2000022-2-2−2i−2i2i2i0000−2i2i000000−2i2i002-20000−2i−2i2i2i22-2-200001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ5422-2-2002−2i2i2-2−2i2i002-2-2000022-2-2−2i−2i2i2i0000−2i2i000000−2i2i002-20000−2i−2i2i2i22-2-20000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ5522-2-2002−2i2i2-2−2i2i002-2-20000-2-222−2i−2i2i2i00002i−2i000000−2i2i002-200002i2i−2i−2i-2-22200001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ5622-2-2002−2i2i2-2−2i2i002-2-20000-2-222−2i−2i2i2i00002i−2i000000−2i2i002-200002i2i−2i−2i-2-2220000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ5722-2-2002−2i2i-222i−2i002-2-22i2i−2i−2i00002i2i−2i−2i000000-220000−2i2i00-222i2i−2i−2i00000000-2-2221+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ5822-2-2002−2i2i-222i−2i002-2-22i2i−2i−2i00002i2i−2i−2i000000-220000−2i2i00-222i2i−2i−2i00000000-2-222−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ5922-2-2002−2i2i-222i−2i002-2-2−2i−2i2i2i00002i2i−2i−2i0000002-20000−2i2i00-22−2i−2i2i2i0000000022-2-21+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ6022-2-2002−2i2i-222i−2i002-2-2−2i−2i2i2i00002i2i−2i−2i0000002-20000−2i2i00-22−2i−2i2i2i0000000022-2-2−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ61444444-244-4-4-4-4-4-4-2-2-20000000022224-4-2-20000-2-222-2-22222000000000000000000000000000000000000000000000000
χ62444444-2-4-4-4-444-4-4-2-2-200000000-2-2-2-2-44-2-2000022-2-2222222000000000000000000000000000000000000000000000000
χ634444-4-4-244-4-4-4-444-2-2-2000000002222-4422000022-2-2-2-2-2-222000000000000000000000000000000000000000000000000
χ644444-4-4-2-4-4-4-44444-2-2-200000000-2-2-2-24-4220000-2-22222-2-222000000000000000000000000000000000000000000000000
χ6544-4-400-24i−4i4-44i−4i00-222000044-4-4−2i−2i2i2i00004i−4i000000−2i2i00-220000−2i−2i2i2i-2-222000000000000000000000000000000000000
χ6644-4-400-24i−4i4-44i−4i00-2220000-4-444−2i−2i2i2i0000−4i4i000000−2i2i00-2200002i2i−2i−2i22-2-2000000000000000000000000000000000000
χ6744-4-400-24i−4i-44−4i4i00-2224i4i−4i−4i00002i2i−2i−2i0000004-40000−2i2i002-2−2i−2i2i2i00000000-2-22200000000000000000000000000000000
χ6844-4-400-24i−4i-44−4i4i00-222−4i−4i4i4i00002i2i−2i−2i000000-440000−2i2i002-22i2i−2i−2i0000000022-2-200000000000000000000000000000000
χ6944-4-400-2−4i4i4-4−4i4i00-222000044-4-42i2i−2i−2i0000−4i4i0000002i−2i00-2200002i2i−2i−2i-2-222000000000000000000000000000000000000
χ7044-4-400-2−4i4i4-4−4i4i00-2220000-4-4442i2i−2i−2i00004i−4i0000002i−2i00-220000−2i−2i2i2i22-2-2000000000000000000000000000000000000
χ7144-4-400-2−4i4i-444i−4i00-2224i4i−4i−4i0000−2i−2i2i2i000000-4400002i−2i002-2−2i−2i2i2i0000000022-2-200000000000000000000000000000000
χ7244-4-400-2−4i4i-444i−4i00-222−4i−4i4i4i0000−2i−2i2i2i0000004-400002i−2i002-22i2i−2i−2i00000000-2-22200000000000000000000000000000000
χ734-44-40040000004i−4i-44-422−2222−22−2i22i2−2i22i20000000000000000004i−4i0022−2222−220000−2i22i2−2i22i2000000000000000000000000000000000000
χ744-44-40040000004i−4i-44-4−2222−22222i2−2i22i2−2i20000000000000000004i−4i00−2222−222200002i2−2i22i2−2i2000000000000000000000000000000000000
χ754-44-4004000000−4i4i-44-422−2222−222i2−2i22i2−2i2000000000000000000−4i4i0022−2222−2200002i2−2i22i2−2i2000000000000000000000000000000000000
χ764-44-4004000000−4i4i-44-4−2222−2222−2i22i2−2i22i2000000000000000000−4i4i00−2222−22220000−2i22i2−2i22i2000000000000000000000000000000000000
χ774-44-400-20000004i−4i2-2222−2222−22−2i22i2−2i22i2−2i32i3−2i32i30000000023−230000−2i2i00−22−226−66−6i2−i2i2−i2i6−i6i6−i600000000000000000000000000000000
χ784-44-400-20000004i−4i2-2222−2222−22−2i22i2−2i22i22i3−2i32i3−2i300000000−23230000−2i2i00−22−22−66−66i2−i2i2−i2−i6i6−i6i600000000000000000000000000000000
χ794-44-400-20000004i−4i2-22−2222−22222i2−2i22i2−2i2−2i32i3−2i32i30000000023−230000−2i2i002−22−2−66−66−i2i2−i2i2−i6i6−i6i600000000000000000000000000000000
χ804-44-400-20000004i−4i2-22−2222−22222i2−2i22i2−2i22i3−2i32i3−2i300000000−23230000−2i2i002−22−26−66−6−i2i2−i2i2i6−i6i6−i600000000000000000000000000000000
χ814-44-400-2000000−4i4i2-2222−2222−222i2−2i22i2−2i2−2i32i3−2i32i300000000−232300002i−2i00−22−22−66−66−i2i2−i2i2i6−i6i6−i600000000000000000000000000000000
χ824-44-400-2000000−4i4i2-2222−2222−222i2−2i22i2−2i22i3−2i32i3−2i30000000023−2300002i−2i00−22−226−66−6−i2i2−i2i2−i6i6−i6i600000000000000000000000000000000
χ834-44-400-2000000−4i4i2-22−2222−2222−2i22i2−2i22i2−2i32i3−2i32i300000000−232300002i−2i002−22−26−66−6i2−i2i2−i2−i6i6−i6i600000000000000000000000000000000
χ844-44-400-2000000−4i4i2-22−2222−2222−2i22i2−2i22i22i3−2i32i3−2i30000000023−2300002i−2i002−22−2−66−66i2−i2i2−i2i6−i6i6−i600000000000000000000000000000000
χ854-4-444-4400000000-4-44−2i22i22i2−2i2−2i22i22i2−2i20000004-400000000000000−2i22i22i2−2i20000−2i22i22i2−2i2000000000000000000000000000000000000
χ864-4-444-4400000000-4-442i2−2i2−2i22i22i2−2i2−2i22i20000004-4000000000000002i2−2i2−2i22i200002i2−2i2−2i22i2000000000000000000000000000000000000
χ874-4-444-4-20000000022-2−2i22i22i2−2i2−2i22i22i2−2i223−23−232300-2200000023−23000000i2−i2−i2i2i6−i6−i6i6i2−i2−i2i2i6−i6−i6i600000000000000000000000000000000
χ884-4-444-4-20000000022-2−2i22i22i2−2i2−2i22i22i2−2i2−232323−2300-22000000−2323000000i2−i2−i2i2−i6i6i6−i6i2−i2−i2i2−i6i6i6−i600000000000000000000000000000000
χ894-4-444-4-20000000022-22i2−2i2−2i22i22i2−2i2−2i22i223−23−232300-2200000023−23000000−i2i2i2−i2−i6i6i6−i6−i2i2i2−i2−i6i6i6−i600000000000000000000000000000000
χ904-4-444-4-20000000022-22i2−2i2−2i22i22i2−2i2−2i22i2−232323−2300-22000000−2323000000−i2i2i2−i2i6−i6−i6i6−i2i2i2−i2i6−i6−i6i600000000000000000000000000000000
χ914-4-44-44400000000-4-44−2i22i22i2−2i22i2−2i2−2i22i2000000-4400000000000000−2i22i22i2−2i200002i2−2i2−2i22i2000000000000000000000000000000000000
χ924-4-44-44400000000-4-442i2−2i2−2i22i2−2i22i22i2−2i2000000-44000000000000002i2−2i2−2i22i20000−2i22i22i2−2i2000000000000000000000000000000000000
χ934-4-44-44-20000000022-2−2i22i22i2−2i22i2−2i2−2i22i223−23−2323002-2000000−2323000000i2−i2−i2i2−i6i6i6−i6−i2i2i2−i2i6−i6−i6i600000000000000000000000000000000
χ944-4-44-44-20000000022-2−2i22i22i2−2i22i2−2i2−2i22i2−232323−23002-200000023−23000000i2−i2−i2i2i6−i6−i6i6−i2i2i2−i2−i6i6i6−i600000000000000000000000000000000
χ954-4-44-44-20000000022-22i2−2i2−2i22i2−2i22i22i2−2i223−23−2323002-2000000−2323000000−i2i2i2−i2i6−i6−i6i6i2−i2−i2i2−i6i6i6−i600000000000000000000000000000000
χ964-4-44-44-20000000022-22i2−2i2−2i22i2−2i22i22i2−2i2−232323−23002-200000023−23000000−i2i2i2−i2−i6i6i6−i6i2−i2−i2i2i6−i6−i6i600000000000000000000000000000000

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