Finite Group Databasebeta

← Group #10693000

Character table — Group #10693000

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order12222222344446662444444444466661212121212126121212121212121212444444444444444444881212121224242424444488
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
χ51111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ61111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1
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−i1-1i−i11-1-1ii−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−ii-1-111−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−iiiii1-1i−i11-1-1ii−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−ii-1-111−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−iiiii1-1−ii11-1-1−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-11i−i-1-111ii−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−i1-1−ii11-1-1−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-11i−i-1-111ii−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
χ1922222222-12222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-1000000
χ2022222222-12222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-211111111000000
χ2122222222-12222-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-11111000000
χ2222222222-12222-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-1000000
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−iiiii00000000000000002-22i−2i-1-111−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−iiiii0000000000000000-22−2i2i11-1-1ii−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−i00000000000000002-2−2i2i-1-111ii−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−i0000000000000000-222i−2i11-1-1−i−iii000000
χ292222-2-222222-2-2222-22-200000000-2-222-2-2-2-222-22000000000000000022-2-222-2-2000000000000000000
χ302222-2-222222-2-2222-22-200000000-2-222-2-2-2-222-220000000000000000-2-222-2-222000000000000000000
χ312222-2-2222-2-222222-2-2222-2-222-2-2-2-2222222-2-2-2-222-2-222-2-20000000000000000000000000000000000
χ322222-2-2222-2-222222-2-22-2-222-2-222-2-2222222-2-2-2-2-2-222-2-2220000000000000000000000000000000000
χ332222-2-222-1-2-222-1-1-1-2-2222-2-222-2-211-1-1-1-1-1-11111-1-111-1-111000000000000000000003−33−33−33−3000000
χ342222-2-222-1-2-222-1-1-1-2-2222-2-222-2-211-1-1-1-1-1-11111-1-111-1-11100000000000000000000−33−33−33−33000000
χ352222-2-222-1-2-222-1-1-1-2-22-2-222-2-22211-1-1-1-1-1-1111111-1-111-1-1000000000000000000003−33−3−33−33000000
χ362222-2-222-1-2-222-1-1-1-2-22-2-222-2-22211-1-1-1-1-1-1111111-1-111-1-100000000000000000000−33−333−33−3000000
χ372222-2-2-2-2222-2-22222-222i2i−2i−2i−2i−2i2i2i-2-2-2-222-2-2222-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ382222-2-2-2-2222-2-22222-22−2i−2i2i2i2i2i−2i−2i-2-2-2-222-2-2222-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ392222-2-2-2-22-2-22222222-200000000-2-2-2-2-2-222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ402222-2-2-2-22-2-22222222-200000000-2-2-2-2-2-222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ412222-2-2-2-2-122-2-2-1-1-12-222i2i−2i−2i−2i−2i2i2i1111-1-111-1-1-11−i−iiiii−i−i000000000000000000003−3−33i3−i3−i3i3000000
χ422222-2-2-2-2-122-2-2-1-1-12-222i2i−2i−2i−2i−2i2i2i1111-1-111-1-1-11−i−iiiii−i−i00000000000000000000−333−3−i3i3i3−i3000000
χ432222-2-2-2-2-122-2-2-1-1-12-22−2i−2i2i2i2i2i−2i−2i1111-1-111-1-1-11ii−i−i−i−iii000000000000000000003−3−33−i3i3i3−i3000000
χ442222-2-2-2-2-122-2-2-1-1-12-22−2i−2i2i2i2i2i−2i−2i1111-1-111-1-1-11ii−i−i−i−iii00000000000000000000−333−3i3−i3−i3i3000000
χ452-2-222-20022i−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+i002i−2i2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ462-2-222-20022i−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+i00−2i2i-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ472-2-222-20022i−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−i002i−2i2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ482-2-222-20022i−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−i00−2i2i-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ492-2-222-2002−2i2i−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−i002i−2i-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ502-2-222-2002−2i2i−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−i00−2i2i2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ512-2-222-2002−2i2i−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+i002i−2i-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ522-2-222-2002−2i2i−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+i00−2i2i2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ532-2-22-220022i−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+i2i−2i00002-21+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ542-2-22-220022i−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−2i2i0000-22−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ552-2-22-220022i−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−i2i−2i00002-2−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ562-2-22-220022i−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−2i2i0000-221+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ572-2-22-22002−2i2i2i−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−i2i−2i0000-22−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ582-2-22-22002−2i2i2i−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−2i2i00002-21−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ592-2-22-22002−2i2i2i−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+i2i−2i0000-221−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ602-2-22-22002−2i2i2i−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−2i2i00002-2−1+i1−i1−i−1+i−1−i1+i1+i−1−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
χ634444-4-444-244-4-4-2-2-2-44-40000000022-2-22222-2-22-2000000000000000000000000000000000000000000
χ644444-4-4-4-4-2-4-444-2-2-244-400000000222222-2-222-2-2000000000000000000000000000000000000000000
χ654-44-4004-440000-4-4400000000000004-4000000000000000000000000000000000000000000002i−2i2i−2i00
χ664-44-4004-440000-4-4400000000000004-400000000000000000000000000000000000000000000−2i2i−2i2i00
χ674-44-400-4440000-4-440000000000000-44000000000000000000000000000000000000000000002i−2i−2i2i00
χ684-44-400-4440000-4-440000000000000-4400000000000000000000000000000000000000000000−2i2i2i−2i00
χ694-4-444-400-24i−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
χ704-4-444-400-24i−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
χ714-4-444-400-2−4i4i−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
χ724-4-444-400-2−4i4i−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
χ734-4-44-4400-24i−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
χ744-4-44-4400-24i−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
χ754-4-44-4400-2−4i4i4i−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
χ764-4-44-4400-2−4i4i4i−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
χ7788-8-8000080000-88-800000000000000000000000000000000000000000000000000000000000000000
χ7888-8-80000-400004-4400000000000000043−43000000000000000000000000000000000000000000000000
χ7988-8-80000-400004-44000000000000000−4343000000000000000000000000000000000000000000000000
χ808-88-8008-8-4000044-40000000000000-4400000000000000000000000000000000000000000000000000
χ818-88-800-88-4000044-400000000000004-400000000000000000000000000000000000000000000000000

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