Finite Group Databasebeta

← Group #10692091

Character table — Group #10692091

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order12222234444446664444444444466121212121212121212121212121212121212444444444444444444881212121224242424888888
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
χ5111111111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111
χ6111111111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ7111111111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1
χ8111111111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111
χ91111-1-1111-1-1-1-11111111-1-1-111-1-1-1-111-1-1-1-111111-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−i1-11-111-1-111-1-1ii−i−ii−i
χ101111-1-1111-1-1-1-11111111-1-1-111-1-1-1-111-1-1-1-111111-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−i-11-11-1-111-1-111−i−iii−ii
χ111111-1-1111-1-1-1-11111111-1-1-111-1-1-1-111-1-1-1-111111-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii1-11-111-1-111-1-1−i−iii−ii
χ121111-1-1111-1-1-1-11111111-1-1-111-1-1-1-111-1-1-1-111111-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii-11-11-1-111-1-111ii−i−ii−i
χ131111-1-1111-1-1-1-111111-1-111-1-1-111-1-111-1-1-1-1111-1-111-1-1-111ii−i−iii−i−i−i−i−i−iiiii1-1-1111-1-1-1-111−i−iiii−i
χ141111-1-1111-1-1-1-111111-1-111-1-1-111-1-111-1-1-1-1111-1-111-1-1-111ii−i−iii−i−i−i−i−i−iiiii-111-1-1-11111-1-1ii−i−i−ii
χ151111-1-1111-1-1-1-111111-1-111-1-1-111-1-111-1-1-1-1111-1-111-1-1-111−i−iii−i−iiiiiii−i−i−i−i1-1-1111-1-1-1-111ii−i−i−ii
χ161111-1-1111-1-1-1-111111-1-111-1-1-111-1-111-1-1-1-1111-1-111-1-1-111−i−iii−i−iiiiiii−i−i−i−i-111-1-1-11111-1-1−i−iiii−i
χ17222222222-2-2-2-2222-2-222222-2-2-2-222-2-2-2-2-2-222-222222-2-2-2-20000000000000000000000000000000000
χ18222222222-2-2-2-2222-2-2-2-2-2-22222222-2-2-2-2-2-222-2-2-2-2-2222220000000000000000000000000000000000
χ192222222-2-222-2-22222-20000-20000222222-2-2-2-2-20000-200002222-2-2-2-200000000000000000000000000
χ202222222-2-222-2-22222-20000-20000222222-2-2-2-2-20000-20000-2-2-2-2222200000000000000000000000000
χ212222222-2-2-2-222222-220000-2000022-2-2-2-222-2-220000-200000000000022-2-222-2-2000000000000000000
χ222222222-2-2-2-222222-220000-2000022-2-2-2-222-2-220000-2000000000000-2-222-2-222000000000000000000
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
χ25222222-1222222-1-1-122-2-2-2-22-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111-11111000000000000000022-2-2-1-1-1-11111000000
χ26222222-1222222-1-1-122-2-2-2-22-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111-111110000000000000000-2-2221111-1-1-1-1000000
χ27222222-122-2-2-2-2-1-1-1-2-222222-2-2-2-2-1-1111111-1-11-1-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i3000000
χ28222222-122-2-2-2-2-1-1-1-2-222222-2-2-2-2-1-1111111-1-11-1-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i3000000
χ29222222-122-2-2-2-2-1-1-1-2-2-2-2-2-222222-1-1111111-1-111111-1-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i3000000
χ30222222-122-2-2-2-2-1-1-1-2-2-2-2-2-222222-1-1111111-1-111111-1-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i3000000
χ312222-2-22222222222-2-222-2-2-2-2-222-2-2-2-2222222-222-2-2-2-2-2220000000000000000000000000000000000
χ322222-2-22222222222-2-2-2-222-222-2-2-2-2-2-2222222-2-2-222-222-2-20000000000000000000000000000000000
χ332222-2-22-2-222-2-2222-22000020000-2-2-2-222-2-2-2-22000020000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ342222-2-22-2-222-2-2222-22000020000-2-2-2-222-2-2-2-2200002000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ352222-2-22-2-2-2-2222222-2000020000-2-222-2-222-2-2-20000200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ362222-2-22-2-2-2-2222222-2000020000-2-222-2-222-2-2-2000020000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ372222-2-2-1222222-1-1-1-2-222-2-2-2-2-2221111-1-1-1-1-1-11-1-111111-1-100000000000000000000−i3i3i3−i3−i3i3i3−i3000000
χ382222-2-2-1222222-1-1-1-2-222-2-2-2-2-2221111-1-1-1-1-1-11-1-111111-1-100000000000000000000i3−i3−i3i3i3−i3−i3i3000000
χ392222-2-2-1222222-1-1-1-2-2-2-222-222-2-21111-1-1-1-1-1-1111-1-11-1-11100000000000000000000−i3i3i3−i3i3−i3−i3i3000000
χ402222-2-2-1222222-1-1-1-2-2-2-222-222-2-21111-1-1-1-1-1-1111-1-11-1-11100000000000000000000i3−i3−i3i3−i3i3i3−i3000000
χ412222-2-2-122-2-2-2-2-1-1-12222-2-2-222-2-211-1-11111-1-1-1-1-1111-1-11100000000000000002-22-2-1-111-1-111000000
χ422222-2-2-122-2-2-2-2-1-1-12222-2-2-222-2-211-1-11111-1-1-1-1-1111-1-1110000000000000000-22-2211-1-111-1-1000000
χ432222-2-2-122-2-2-2-2-1-1-122-2-222-2-2-22211-1-11111-1-1-111-1-1111-1-100000000000000002-2-22-1-11111-1-1000000
χ442222-2-2-122-2-2-2-2-1-1-122-2-222-2-2-22211-1-11111-1-1-111-1-1111-1-10000000000000000-222-211-1-1-1-111000000
χ452-2-220022-22i−2i2i−2i-2-2200002i−2i02-20000002i−2i2i−2i2-20002i−2i02-2001+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ462-2-220022-22i−2i2i−2i-2-2200002i−2i02-20000002i−2i2i−2i2-20002i−2i02-200−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ472-2-220022-22i−2i2i−2i-2-220000−2i2i0-220000002i−2i2i−2i2-2000−2i2i0-22001+i−1−i1−i−1+i1+i−1−i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ482-2-220022-22i−2i2i−2i-2-220000−2i2i0-220000002i−2i2i−2i2-2000−2i2i0-2200−1−i1+i−1+i1−i−1−i1+i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ492-2-220022-2−2i2i−2i2i-2-2200002i−2i0-22000000−2i2i−2i2i2-20002i−2i0-22001−i−1+i1+i−1−i1−i−1+i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ502-2-220022-2−2i2i−2i2i-2-2200002i−2i0-22000000−2i2i−2i2i2-20002i−2i0-2200−1+i1−i−1−i1+i−1+i1−i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ512-2-220022-2−2i2i−2i2i-2-220000−2i2i02-2000000−2i2i−2i2i2-2000−2i2i02-2001−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ522-2-220022-2−2i2i−2i2i-2-220000−2i2i02-2000000−2i2i−2i2i2-2000−2i2i02-200−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ532-2-22002-222i−2i−2i2i-2-22002i−2i000002-200002i−2i−2i2i-2202i−2i000002-21+i−1−i1−i−1+i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ542-2-22002-222i−2i−2i2i-2-22002i−2i000002-200002i−2i−2i2i-2202i−2i000002-2−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ552-2-22002-222i−2i−2i2i-2-2200−2i2i00000-2200002i−2i−2i2i-220−2i2i00000-221+i−1−i1−i−1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ562-2-22002-222i−2i−2i2i-2-2200−2i2i00000-2200002i−2i−2i2i-220−2i2i00000-22−1−i1+i−1+i1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ572-2-22002-22−2i2i2i−2i-2-22002i−2i00000-220000−2i2i2i−2i-2202i−2i00000-221−i−1+i1+i−1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ582-2-22002-22−2i2i2i−2i-2-22002i−2i00000-220000−2i2i2i−2i-2202i−2i00000-22−1+i1−i−1−i1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ592-2-22002-22−2i2i2i−2i-2-2200−2i2i000002-20000−2i2i2i−2i-220−2i2i000002-21−i−1+i1+i−1−i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ602-2-22002-22−2i2i2i−2i-2-2200−2i2i000002-20000−2i2i2i−2i-220−2i2i000002-2−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ61444444-2-4-444-4-4-2-2-24-40000-40000-2-2-2-2-2-2222220000200000000000000000000000000000000000000
χ62444444-2-4-4-4-444-2-2-2-440000-40000-2-22222-2-222-20000200000000000000000000000000000000000000
χ634444-4-4-2-4-444-4-4-2-2-2-440000400002222-2-22222-20000-200000000000000000000000000000000000000
χ644444-4-4-2-4-4-4-444-2-2-24-400004000022-2-222-2-22220000-200000000000000000000000000000000000000
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
χ694-4-4400-24-44i−4i4i−4i22-200004i−4i04-4000000−2i2i−2i2i-22000−2i2i0-22000000000000000000000000000000000000
χ704-4-4400-24-44i−4i4i−4i22-20000−4i4i0-44000000−2i2i−2i2i-220002i−2i02-2000000000000000000000000000000000000
χ714-4-4400-24-4−4i4i−4i4i22-200004i−4i0-440000002i−2i2i−2i-22000−2i2i02-2000000000000000000000000000000000000
χ724-4-4400-24-4−4i4i−4i4i22-20000−4i4i04-40000002i−2i2i−2i-220002i−2i0-22000000000000000000000000000000000000
χ734-4-4400-2-444i−4i−4i4i22-2004i−4i000004-40000−2i2i2i−2i2-20−2i2i00000-220000000000000000000000000000000000
χ744-4-4400-2-444i−4i−4i4i22-200−4i4i00000-440000−2i2i2i−2i2-202i−2i000002-20000000000000000000000000000000000
χ754-4-4400-2-44−4i4i4i−4i22-2004i−4i00000-4400002i−2i−2i2i2-20−2i2i000002-20000000000000000000000000000000000
χ764-4-4400-2-44−4i4i4i−4i22-200−4i4i000004-400002i−2i−2i2i2-202i−2i00000-220000000000000000000000000000000000
χ7788-8-88-8-4000000-44400000000000-440000000000000000000000000000000000000000000000000000
χ7888-8-8-88-4000000-444000000000004-40000000000000000000000000000000000000000000000000000
χ798-88-8008000000-88-800000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-40000004-440000000000000−4i34i300000000000000000000000000000000000000000000000000
χ818-88-800-40000004-4400000000000004i3−4i300000000000000000000000000000000000000000000000000

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