Finite Group Databasebeta

← Group #10692084

Character table — Group #10692084

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order1222223444444666222244444446612121212121212126666121212121212444444444444444444881212121224242424888888
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
χ51111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111
χ61111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ71111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1
χ81111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111
χ91111-1-1111-1-1-1-111111-1-11-1111-1-1-1-1-1-111-1-11111-1-11-111-1-1ii−i−iii−i−iiiii−i−i−i−i1-11-111-1-111-1-1ii−i−ii−i
χ101111-1-1111-1-1-1-111111-1-11-1111-1-1-1-1-1-111-1-11111-1-11-111-1-1ii−i−iii−i−iiiii−i−i−i−i-11-11-1-111-1-111−i−iii−ii
χ111111-1-1111-1-1-1-111111-1-11-1111-1-1-1-1-1-111-1-11111-1-11-111-1-1−i−iii−i−iii−i−i−i−iiiii1-11-111-1-111-1-1−i−iii−ii
χ121111-1-1111-1-1-1-111111-1-11-1111-1-1-1-1-1-111-1-11111-1-11-111-1-1−i−iii−i−iii−i−i−i−iiiii-11-11-1-111-1-111ii−i−ii−i
χ131111-1-1111-1-1-1-1111-1-1111-11-1-111-1-1-1-111-1-111-1-1111-1-1-111ii−i−iii−i−i−i−i−i−iiiii1-1-1111-1-1-1-111−i−iiii−i
χ141111-1-1111-1-1-1-1111-1-1111-11-1-111-1-1-1-111-1-111-1-1111-1-1-111ii−i−iii−i−i−i−i−i−iiiii-111-1-1-11111-1-1ii−i−i−ii
χ151111-1-1111-1-1-1-1111-1-1111-11-1-111-1-1-1-111-1-111-1-1111-1-1-111−i−iii−i−iiiiiii−i−i−i−i1-1-1111-1-1-1-111ii−i−i−ii
χ161111-1-1111-1-1-1-1111-1-1111-11-1-111-1-1-1-111-1-111-1-1111-1-1-111−i−iii−i−iiiiiii−i−i−i−i-111-1-1-11111-1-1−i−iiii−i
χ17222222222-2-2-2-22222222-22-2-2-2-2-222-2-2-2-2-2-2222222-22-2-2-2-20000000000000000000000000000000000
χ18222222222-2-2-2-2222-2-2-2-2-22-2222222-2-2-2-2-2-222-2-2-2-2-2222220000000000000000000000000000000000
χ192222222-2-222-2-222200002-2-200002222-2-2-2-2-2-200002-200000000000022-2-222-2-2000000000000000000
χ202222222-2-222-2-222200002-2-200002222-2-2-2-2-2-200002-2000000000000-2-222-2-222000000000000000000
χ212222222-2-2-2-2222220000-2-22000022-2-22222-2-20000-2-200002222-2-2-2-200000000000000000000000000
χ222222222-2-2-2-2222220000-2-22000022-2-22222-2-20000-2-20000-2-2-2-2222200000000000000000000000000
χ23222222-1222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-1000000
χ24222222-1222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-211111111000000
χ25222222-1222222-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111-1-11111000000000000000022-2-2-1-1-1-11111000000
χ26222222-1222222-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111-1-111110000000000000000-2-2221111-1-1-1-1000000
χ27222222-122-2-2-2-2-1-1-12222-22-2-2-2-2-2-1-1111111-1-1-1-1-1-11-1111100000000000000000000−i3i3−i3i3−i3i3−i3i3000000
χ28222222-122-2-2-2-2-1-1-12222-22-2-2-2-2-2-1-1111111-1-1-1-1-1-11-1111100000000000000000000i3−i3i3−i3i3−i3i3−i3000000
χ29222222-122-2-2-2-2-1-1-1-2-2-2-2-22-22222-1-1111111-1-111111-1-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i3000000
χ30222222-122-2-2-2-2-1-1-1-2-2-2-2-22-22222-1-1111111-1-111111-1-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i3000000
χ312222-2-2222222222222-2-2-2-2-2-2-222-2-222-2-2222222-2-2-2-2-2-2220000000000000000000000000000000000
χ322222-2-22222222222-2-222-2-2-222-2-2-2-222-2-22222-2-222-2-222-2-20000000000000000000000000000000000
χ332222-2-22-2-222-2-22220000-2220000-2-22222-2-2-2-20000-2200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ342222-2-22-2-222-2-22220000-2220000-2-22222-2-2-2-20000-220000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ352222-2-22-2-2-2-222222000022-20000-2-2-2-2-2-222-2-20000220000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ362222-2-22-2-2-2-222222000022-20000-2-2-2-2-2-222-2-2000022000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ372222-2-2-1222222-1-1-122-2-2-2-2-2-2-22211-1-111-1-1-1-1-1-1111111-1-100000000000000000000−i3i3i3−i3−i3i3i3−i3000000
χ382222-2-2-1222222-1-1-122-2-2-2-2-2-2-22211-1-111-1-1-1-1-1-1111111-1-100000000000000000000i3−i3−i3i3i3−i3−i3i3000000
χ392222-2-2-1222222-1-1-1-2-222-2-2-222-2-211-1-111-1-1-1-111-1-111-1-11100000000000000000000−i3i3i3−i3i3−i3−i3i3000000
χ402222-2-2-1222222-1-1-1-2-222-2-2-222-2-211-1-111-1-1-1-111-1-111-1-11100000000000000000000i3−i3−i3i3−i3i3i3−i3000000
χ412222-2-2-122-2-2-2-2-1-1-122-2-22-2222-2-21111-1-111-1-1-1-111-11-1-11100000000000000002-22-2-1-111-1-111000000
χ422222-2-2-122-2-2-2-2-1-1-122-2-22-2222-2-21111-1-111-1-1-1-111-11-1-1110000000000000000-22-2211-1-111-1-1000000
χ432222-2-2-122-2-2-2-2-1-1-1-2-2222-22-2-2221111-1-111-1-111-1-1-1111-1-100000000000000002-2-22-1-11111-1-1000000
χ442222-2-2-122-2-2-2-2-1-1-1-2-2222-22-2-2221111-1-111-1-111-1-1-1111-1-10000000000000000-222-211-1-1-1-111000000
χ452-22-20022-22i−2i2i−2i-22-2002-20002i−2i00002i−2i002i−2i2-2002-2002i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ462-22-20022-22i−2i2i−2i-22-2002-20002i−2i00002i−2i002i−2i2-2002-2002i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ472-22-20022-22i−2i2i−2i-22-200-22000−2i2i00002i−2i002i−2i2-200-2200−2i2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ482-22-20022-22i−2i2i−2i-22-200-22000−2i2i00002i−2i002i−2i2-200-2200−2i2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ492-22-20022-2−2i2i−2i2i-22-2002-2000−2i2i0000−2i2i00−2i2i2-2002-200−2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ502-22-20022-2−2i2i−2i2i-22-2002-2000−2i2i0000−2i2i00−2i2i2-2002-200−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ512-22-20022-2−2i2i−2i2i-22-200-220002i−2i0000−2i2i00−2i2i2-200-22002i−2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ522-22-20022-2−2i2i−2i2i-22-200-220002i−2i0000−2i2i00−2i2i2-200-22002i−2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ532-22-2002-222i−2i−2i2i-22-22-200000002i−2i002i−2i00−2i2i-222-20000002i−2i1−i−1+i1+i−1−i−1+i1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ542-22-2002-222i−2i−2i2i-22-22-200000002i−2i002i−2i00−2i2i-222-20000002i−2i−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ552-22-2002-222i−2i−2i2i-22-2-220000000−2i2i002i−2i00−2i2i-22-22000000−2i2i1−i−1+i1+i−1−i−1+i1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ562-22-2002-222i−2i−2i2i-22-2-220000000−2i2i002i−2i00−2i2i-22-22000000−2i2i−1+i1−i−1−i1+i1−i−1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ572-22-2002-22−2i2i2i−2i-22-22-20000000−2i2i00−2i2i002i−2i-222-2000000−2i2i1+i−1−i1−i−1+i−1−i1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ582-22-2002-22−2i2i2i−2i-22-22-20000000−2i2i00−2i2i002i−2i-222-2000000−2i2i−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ592-22-2002-22−2i2i2i−2i-22-2-2200000002i−2i00−2i2i002i−2i-22-220000002i−2i1+i−1−i1−i−1+i−1−i1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ602-22-2002-22−2i2i2i−2i-22-2-2200000002i−2i00−2i2i002i−2i-22-220000002i−2i−1−i1+i−1+i1−i1+i−1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ61444444-2-4-444-4-4-2-2-200004-4-40000-2-2-2-22222220000-2200000000000000000000000000000000000000
χ62444444-2-4-4-4-444-2-2-20000-4-440000-2-222-2-2-2-22200002200000000000000000000000000000000000000
χ634444-4-4-2-4-444-4-4-2-2-20000-444000022-2-2-2-2222200002-200000000000000000000000000000000000000
χ644444-4-4-2-4-4-4-444-2-2-2000044-40000222222-2-2220000-2-200000000000000000000000000000000000000
χ6544-4-44-440000004-4-4000000000004-400000000000000000000000000000000000000000000002-22-200
χ6644-4-44-440000004-4-4000000000004-40000000000000000000000000000000000000000000000-22-2200
χ6744-4-4-4440000004-4-400000000000-4400000000000000000000000000000000000000000000002i−2i−2i2i00
χ6844-4-4-4440000004-4-400000000000-440000000000000000000000000000000000000000000000−2i2i2i−2i00
χ694-44-400-24-44i−4i4i−4i2-22004-40004i−4i0000−2i2i00−2i2i-2200-2200−2i2i000000000000000000000000000000000000
χ704-44-400-24-44i−4i4i−4i2-2200-44000−4i4i0000−2i2i00−2i2i-22002-2002i−2i000000000000000000000000000000000000
χ714-44-400-24-4−4i4i−4i4i2-22004-4000−4i4i00002i−2i002i−2i-2200-22002i−2i000000000000000000000000000000000000
χ724-44-400-24-4−4i4i−4i4i2-2200-440004i−4i00002i−2i002i−2i-22002-200−2i2i000000000000000000000000000000000000
χ734-44-400-2-444i−4i−4i4i2-224-400000004i−4i00−2i2i002i−2i2-2-22000000−2i2i0000000000000000000000000000000000
χ744-44-400-2-444i−4i−4i4i2-22-440000000−4i4i00−2i2i002i−2i2-22-20000002i−2i0000000000000000000000000000000000
χ754-44-400-2-44−4i4i4i−4i2-224-40000000−4i4i002i−2i00−2i2i2-2-220000002i−2i0000000000000000000000000000000000
χ764-44-400-2-44−4i4i4i−4i2-22-4400000004i−4i002i−2i00−2i2i2-22-2000000−2i2i0000000000000000000000000000000000
χ7788-8-88-8-4000000-44400000000000-440000000000000000000000000000000000000000000000000000
χ7888-8-8-88-4000000-444000000000004-40000000000000000000000000000000000000000000000000000
χ798-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-400000044-4000000000000000−4i34i3000000000000000000000000000000000000000000000000
χ818-8-8800-400000044-40000000000000004i3−4i3000000000000000000000000000000000000000000000000

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