Finite Group Databasebeta

← Group #10693064

Character table — Group #10693064

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order122222344444466622444444444661212121212121212661212121212121212888888888888888888882424242424242424444444
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
χ51111111111111111-1-1-1-1111-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ61111111111111111-1-1-1-1111-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111-1-1-1-1111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111-1-1-1-1111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1
χ91111111-1-1-1-1-1-1111111111-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i11-1-11-1
χ101111111-1-1-1-1-1-1111111111-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-1-111-11
χ111111111-1-1-1-1-1-1111111111-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i-1-111-11
χ121111111-1-1-1-1-1-1111111111-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii11-1-11-1
χ131111111-1-1-1-1-1-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii11-1-1-11
χ141111111-1-1-1-1-1-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-1-1111-1
χ151111111-1-1-1-1-1-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-1-1111-1
χ161111111-1-1-1-1-1-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i11-1-1-11
χ1722222222222-2-222222-2-2-2-2-222-2-222-2-2-2-2222222-2-2-2-222-2-20000000000000000000000000000000000
χ1822222222222-2-2222-2-222-2-2-2-2-22222-2-2-2-22222-2-2-2-222-2-2220000000000000000000000000000000000
χ192222222-2-2-2-22222222-2-2-2-22-2-222222222-2-2-2-222-2-2-2-2-2-2220000000000000000000000000000000000
χ202222222-2-2-2-222222-2-222-2-2222-2-2222222-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000
χ21222222-1222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-1000000
χ22222222-1222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-211111111000000
χ23222222-1222222-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-111-1-1111111000000000000000022-2-2-1-1-1-11111000000
χ24222222-1222222-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-111-1-11111110000000000000000-2-2221111-1-1-1-1000000
χ25222222-12222-2-2-1-1-122-2-2-2-2-222-2-2-1-11111-1-1-1-1-1-11111-1-11100000000000000000000−i3i3−i3i3−i3i3−i3i3000000
χ26222222-12222-2-2-1-1-122-2-2-2-2-222-2-2-1-11111-1-1-1-1-1-11111-1-11100000000000000000000i3−i3i3−i3i3−i3i3−i3000000
χ27222222-12222-2-2-1-1-1-2-222-2-2-2-2-222-1-11111-1-1-1-11111-1-111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i3000000
χ28222222-12222-2-2-1-1-1-2-222-2-2-2-2-222-1-11111-1-1-1-11111-1-111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i3000000
χ29222222-1-2-2-2-222-1-1-122-2-2-2-22-2-222-1-1-1-1-1-11111-1-1111111-1-1000000000000000000003−3−333−3−33000000
χ30222222-1-2-2-2-222-1-1-122-2-2-2-22-2-222-1-1-1-1-1-11111-1-1111111-1-100000000000000000000−333−3−333−3000000
χ31222222-1-2-2-2-222-1-1-1-2-222-2-2222-2-2-1-1-1-1-1-111111111-1-1-1-111000000000000000000003−3−33−333−3000000
χ32222222-1-2-2-2-222-1-1-1-2-222-2-2222-2-2-1-1-1-1-1-111111111-1-1-1-11100000000000000000000−333−33−3−33000000
χ33222222-1-2-2-2-2-2-2-1-1-1222222-2-2-2-2-2-1-111111111-1-1-1-1-1-1111100000000000000002i−2i2i−2i−i−iii−i−iii000000
χ34222222-1-2-2-2-2-2-2-1-1-1222222-2-2-2-2-2-1-111111111-1-1-1-1-1-111110000000000000000−2i2i−2i2iii−i−iii−i−i000000
χ35222222-1-2-2-2-2-2-2-1-1-1-2-2-2-222-22222-1-11111111111-1-111-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i000000
χ36222222-1-2-2-2-2-2-2-1-1-1-2-2-2-222-22222-1-11111111111-1-111-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii000000
χ372222-2-2222-2-22222200002-2-20000-2-222-2-222-2-2002-20000000000000022-2-222-2-2000000000000000000
χ382222-2-2222-2-22222200002-2-20000-2-222-2-222-2-2002-200000000000000-2-222-2-222000000000000000000
χ392222-2-2222-2-2-2-22220000-2220000-2-2-2-22222-2-200-220000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ402222-2-2222-2-2-2-22220000-2220000-2-2-2-22222-2-200-22000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ412222-2-22-2-222222220000-22-20000-2-222-2-2-2-22200-2200000022-2-2-2-22200000000000000000000000000
χ422222-2-22-2-222222220000-22-20000-2-222-2-2-2-22200-22000000-2-22222-2-200000000000000000000000000
χ432222-2-22-2-222-2-222200002-220000-2-2-2-222-2-222002-2000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ442222-2-22-2-222-2-222200002-220000-2-2-2-222-2-222002-200000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ452-22-22-222i−2i2i−2i002-2-2002i−2i000002-22-200002i−2i2i−2i00002i−2i002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ462-22-22-222i−2i2i−2i002-2-2002i−2i000002-22-200002i−2i2i−2i00002i−2i002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ472-22-22-222i−2i2i−2i002-2-200−2i2i00000-222-200002i−2i2i−2i0000−2i2i00-221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ482-22-22-222i−2i2i−2i002-2-200−2i2i00000-222-200002i−2i2i−2i0000−2i2i00-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ492-22-22-22−2i2i−2i2i002-2-2002i−2i00000-222-20000−2i2i−2i2i00002i−2i00-221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ502-22-22-22−2i2i−2i2i002-2-2002i−2i00000-222-20000−2i2i−2i2i00002i−2i00-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ512-22-22-22−2i2i−2i2i002-2-200−2i2i000002-22-20000−2i2i−2i2i0000−2i2i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ522-22-22-22−2i2i−2i2i002-2-200−2i2i000002-22-20000−2i2i−2i2i0000−2i2i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ532-22-2-2222i−2i−2i2i002-2-22-2000002i−2i00-2200002i−2i−2i2i2-200002i−2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ542-22-2-2222i−2i−2i2i002-2-22-2000002i−2i00-2200002i−2i−2i2i2-200002i−2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ552-22-2-2222i−2i−2i2i002-2-2-2200000−2i2i00-2200002i−2i−2i2i-220000−2i2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ562-22-2-2222i−2i−2i2i002-2-2-2200000−2i2i00-2200002i−2i−2i2i-220000−2i2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ572-22-2-222−2i2i2i−2i002-2-22-200000−2i2i00-220000−2i2i2i−2i2-20000−2i2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ582-22-2-222−2i2i2i−2i002-2-22-200000−2i2i00-220000−2i2i2i−2i2-20000−2i2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ592-22-2-222−2i2i2i−2i002-2-2-22000002i−2i00-220000−2i2i2i−2i-2200002i−2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ602-22-2-222−2i2i2i−2i002-2-2-22000002i−2i00-220000−2i2i2i−2i-2200002i−2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ614444-4-4-244-4-444-2-2-200004-4-4000022-2-222-2-22200-220000000000000000000000000000000000000000
χ624444-4-4-244-4-4-4-4-2-2-20000-44400002222-2-2-2-222002-20000000000000000000000000000000000000000
χ634444-4-4-2-4-44444-2-2-20000-44-4000022-2-22222-2-2002-20000000000000000000000000000000000000000
χ644444-4-4-2-4-444-4-4-2-2-200004-4400002222-2-222-2-200-220000000000000000000000000000000000000000
χ654-44-44-4-24i−4i4i−4i00-222004i−4i000004-4-220000−2i2i−2i2i0000−2i2i00-220000000000000000000000000000000000
χ664-44-44-4-24i−4i4i−4i00-22200−4i4i00000-44-220000−2i2i−2i2i00002i−2i002-20000000000000000000000000000000000
χ674-44-44-4-2−4i4i−4i4i00-222004i−4i00000-44-2200002i−2i2i−2i0000−2i2i002-20000000000000000000000000000000000
χ684-44-44-4-2−4i4i−4i4i00-22200−4i4i000004-4-2200002i−2i2i−2i00002i−2i00-220000000000000000000000000000000000
χ694-44-4-44-24i−4i−4i4i00-2224-4000004i−4i002-20000−2i2i2i−2i-220000−2i2i000000000000000000000000000000000000
χ704-44-4-44-24i−4i−4i4i00-222-4400000−4i4i002-20000−2i2i2i−2i2-200002i−2i000000000000000000000000000000000000
χ714-44-4-44-2−4i4i4i−4i00-2224-400000−4i4i002-200002i−2i−2i2i-2200002i−2i000000000000000000000000000000000000
χ724-44-4-44-2−4i4i4i−4i00-222-44000004i−4i002-200002i−2i−2i2i2-20000−2i2i000000000000000000000000000000000000
χ734-4-4400400004i−4i-44-400000000000004i−4i000000000000000000000000000000000000000000002i−2i2-200
χ744-4-4400400004i−4i-44-400000000000004i−4i00000000000000000000000000000000000000000000−2i2i-2200
χ754-4-440040000−4i4i-44-40000000000000−4i4i000000000000000000000000000000000000000000002i−2i-2200
χ764-4-440040000−4i4i-44-40000000000000−4i4i00000000000000000000000000000000000000000000−2i2i2-200
χ7788-8-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ7888-8-800-400000044-400000000000000043−43000000000000000000000000000000000000000000000000
χ7988-8-800-400000044-4000000000000000−4343000000000000000000000000000000000000000000000000
χ808-8-8800-400008i−8i4-440000000000000−4i4i00000000000000000000000000000000000000000000000000
χ818-8-8800-40000−8i8i4-4400000000000004i−4i00000000000000000000000000000000000000000000000000

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