Finite Group Databasebeta

← Group #10692629

Character table — Group #10692629

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order122222223444466624444444444666612121212121261212121212121212122222444444444444246688121224242424444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1
χ61111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ71111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111
χ81111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1
χ9111111-1-11-1-1-1-1111-111iiii−i−i−i−i11-1-111-1-1-1-1-11iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i1-111i−i-1-1ii−i−i11-1-1i−i
χ10111111-1-11-1-1-1-1111-111iiii−i−i−i−i11-1-111-1-1-1-1-11iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i-11-1-1−ii11−i−iii-1-111−ii
χ11111111-1-11-1-1-1-1111-111iiii−i−i−i−i11-1-111-1-1-1-1-11iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii1-111i−i-1-1ii−i−i-1-111−ii
χ12111111-1-11-1-1-1-1111-111iiii−i−i−i−i11-1-111-1-1-1-1-11iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii-11-1-1−ii11−i−iii11-1-1i−i
χ13111111-1-11-1-1-1-1111-111−i−i−i−iiiii11-1-111-1-1-1-1-11−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii1-111−ii-1-1−i−iii11-1-1−ii
χ14111111-1-11-1-1-1-1111-111−i−i−i−iiiii11-1-111-1-1-1-1-11−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii-11-1-1i−i11ii−i−i-1-111i−i
χ15111111-1-11-1-1-1-1111-111−i−i−i−iiiii11-1-111-1-1-1-1-11−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i1-111−ii-1-1−i−iii-1-111i−i
χ16111111-1-11-1-1-1-1111-111−i−i−i−iiiii11-1-111-1-1-1-1-11−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i-11-1-1i−i11ii−i−i11-1-1−ii
χ17222222222-2-2-2-22222-2-2000000002222-2-2-2-2-2-22-2000000002222-2-2-2-200000000000000000000000000
χ18222222222-2-2-2-22222-2-2000000002222-2-2-2-2-2-22-200000000-2-2-2-2222200000000000000000000000000
χ1922222222-12222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-122-1-1-1-1-1-1000000
χ2022222222-12222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-211-2-2111111000000
χ2122222222-12222-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000000022-1-1-2-2-1-11111000000
χ2222222222-12222-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2112211-1-1-1-1000000
χ23222222-2-222222222-2-2-20000000022-2-2-2-22222-2-20000000022-2-2-2-22200000000000000000000000000
χ24222222-2-222222222-2-2-20000000022-2-2-2-22222-2-200000000-2-22222-2-200000000000000000000000000
χ25222222-2-2-1-2-2-2-2-1-1-1-2222i2i2i2i−2i−2i−2i−2i-1-111-1-111111-1−i−i−i−iiiii00000000000000002-2-1-12i−2i11−i−iii000000
χ26222222-2-2-1-2-2-2-2-1-1-1-2222i2i2i2i−2i−2i−2i−2i-1-111-1-111111-1−i−i−i−iiiii0000000000000000-2211−2i2i-1-1ii−i−i000000
χ27222222-2-2-1-2-2-2-2-1-1-1-222−2i−2i−2i−2i2i2i2i2i-1-111-1-111111-1iiii−i−i−i−i00000000000000002-2-1-1−2i2i11ii−i−i000000
χ28222222-2-2-1-2-2-2-2-1-1-1-222−2i−2i−2i−2i2i2i2i2i-1-111-1-111111-1iiii−i−i−i−i0000000000000000-22112i−2i-1-1−i−iii000000
χ292222-2-222222-2-2222-22-222-2-222-2-2-2-222-2-2-2-222-2222-2-222-2-20000000000000000000000000000000000
χ302222-2-222222-2-2222-22-2-2-222-2-222-2-222-2-2-2-222-22-2-222-2-2220000000000000000000000000000000000
χ312222-2-2222-2-222222-2-2200000000-2-2222222-2-2-2-2000000000000000022-2-222-2-2000000000000000000
χ322222-2-2222-2-222222-2-2200000000-2-2222222-2-2-2-20000000000000000-2-222-2-222000000000000000000
χ332222-2-222-122-2-2-1-1-1-22-222-2-222-2-211-1-11111-1-11-1-1-111-1-111000000000000000000−i3i300−i3i3−i3i3−i3i3000000
χ342222-2-222-122-2-2-1-1-1-22-222-2-222-2-211-1-11111-1-11-1-1-111-1-111000000000000000000i3−i300i3−i3i3−i3i3−i3000000
χ352222-2-222-122-2-2-1-1-1-22-2-2-222-2-22211-1-11111-1-11-111-1-111-1-1000000000000000000−i3i300−i3i3i3−i3i3−i3000000
χ362222-2-222-122-2-2-1-1-1-22-2-2-222-2-22211-1-11111-1-11-111-1-111-1-1000000000000000000i3−i300i3−i3−i3i3−i3i3000000
χ372222-2-2-2-2222-2-22222-2200000000-2-2-2-222-2-2222-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ382222-2-2-2-2222-2-22222-2200000000-2-2-2-222-2-2222-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ392222-2-2-2-22-2-22222222-22i2i−2i−2i−2i−2i2i2i-2-2-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ402222-2-2-2-22-2-22222222-2−2i−2i2i2i2i2i−2i−2i-2-2-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ412222-2-2-2-2-1-2-222-1-1-122-22i2i−2i−2i−2i−2i2i2i111111-1-111-1-1−i−iiiii−i−i000000000000000000−i3i300i3−i33−3−33000000
χ422222-2-2-2-2-1-2-222-1-1-122-22i2i−2i−2i−2i−2i2i2i111111-1-111-1-1−i−iiiii−i−i000000000000000000i3−i300−i3i3−333−3000000
χ432222-2-2-2-2-1-2-222-1-1-122-2−2i−2i2i2i2i2i−2i−2i111111-1-111-1-1ii−i−i−i−iii000000000000000000−i3i300i3−i3−333−3000000
χ442222-2-2-2-2-1-2-222-1-1-122-2−2i−2i2i2i2i2i−2i−2i111111-1-111-1-1ii−i−i−i−iii000000000000000000i3−i300−i3i33−3−33000000
χ4522-2-22-20022i−2i2i−2i2-2-20001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-200002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i002-22i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ4622-2-22-20022i−2i2i−2i2-2-20001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-200002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i00-22−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ4722-2-22-20022i−2i2i−2i2-2-2000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i002-22i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ4822-2-22-20022i−2i2i−2i2-2-2000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i00-22−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ4922-2-22-2002−2i2i−2i2i2-2-20001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-20000−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i002-2−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ5022-2-22-2002−2i2i−2i2i2-2-20001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-20000−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i00-222i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ5122-2-22-2002−2i2i−2i2i2-2-2000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-20000−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i002-2−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ5222-2-22-2002−2i2i−2i2i2-2-2000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-20000−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i00-222i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ5322-2-2-220022i−2i−2i2i2-2-20001+i−1−i−1−i1+i1−i−1+i−1+i1−i-220000−2i2i2i−2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i2-200002i−2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ5422-2-2-220022i−2i−2i2i2-2-20001+i−1−i−1−i1+i1−i−1+i−1+i1−i-220000−2i2i2i−2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i-220000−2i2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ5522-2-2-220022i−2i−2i2i2-2-2000−1−i1+i1+i−1−i−1+i1−i1−i−1+i-220000−2i2i2i−2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i2-200002i−2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ5622-2-2-220022i−2i−2i2i2-2-2000−1−i1+i1+i−1−i−1+i1−i1−i−1+i-220000−2i2i2i−2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i-220000−2i2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ5722-2-2-22002−2i2i2i−2i2-2-20001−i−1+i−1+i1−i1+i−1−i−1−i1+i-2200002i−2i−2i2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i2-20000−2i2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ5822-2-2-22002−2i2i2i−2i2-2-20001−i−1+i−1+i1−i1+i−1−i−1−i1+i-2200002i−2i−2i2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i-2200002i−2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ5922-2-2-22002−2i2i2i−2i2-2-2000−1+i1−i1−i−1+i−1−i1+i1+i−1−i-2200002i−2i−2i2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i2-20000−2i2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ6022-2-2-22002−2i2i2i−2i2-2-2000−1+i1−i1−i−1+i−1−i1+i1+i−1−i-2200002i−2i−2i2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i-2200002i−2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ6144444444-2-4-4-4-4-2-2-24-4-400000000-2-2-2-2222222-22000000000000000000000000000000000000000000
χ62444444-4-4-24444-2-2-2-4-4-400000000-2-22222-2-2-2-222000000000000000000000000000000000000000000
χ634444-4-444-2-4-444-2-2-2-4-440000000022-2-2-2-2-2-22222000000000000000000000000000000000000000000
χ644444-4-4-4-4-244-4-4-2-2-24-44000000002222-2-222-2-2-22000000000000000000000000000000000000000000
χ6544-4-44-400-24i−4i4i−4i-2220002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i-220000−2i2i−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000000000000000
χ6644-4-44-400-24i−4i4i−4i-222000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i-220000−2i2i−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000000000000000
χ6744-4-44-400-2−4i4i−4i4i-2220002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i-2200002i−2i2i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000000000000000
χ6844-4-44-400-2−4i4i−4i4i-222000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i-2200002i−2i2i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000000000000000
χ6944-4-4-4400-24i−4i−4i4i-2220002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i2-200002i−2i−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000000000000000000000
χ7044-4-4-4400-24i−4i−4i4i-222000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i2-200002i−2i−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000000000000000000000
χ7144-4-4-4400-2−4i4i4i−4i-2220002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i2-20000−2i2i2i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000000000000000000000
χ7244-4-4-4400-2−4i4i4i−4i-222000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i2-20000−2i2i2i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000000000000000000000
χ734-4-44004-440000-44-400000000000004-4000000000000000000000000000000000000000000002-22-200
χ744-4-44004-440000-44-400000000000004-400000000000000000000000000000000000000000000-22-2200
χ754-4-4400-4440000-44-40000000000000-44000000000000000000000000000000000000000000002-2-2200
χ764-4-4400-4440000-44-40000000000000-4400000000000000000000000000000000000000000000-222-200
χ778-88-8000080000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ788-88-80000-4000044-4000000000000000−4i34i3000000000000000000000000000000000000000000000000
χ798-88-80000-4000044-40000000000000004i3−4i3000000000000000000000000000000000000000000000000
χ808-8-88008-8-400004-440000000000000-4400000000000000000000000000000000000000000000000000
χ818-8-8800-88-400004-4400000000000004-400000000000000000000000000000000000000000000000000

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