Finite Group Databasebeta

← Group #10691965

Character table — Group #10691965

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order122222344444466644444444444661212121212121212121212121212121212128888888888888888246688121224242424888844
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
χ91111-1-111-11-1-1-111111-111-1-111-1-1-1-111-1-11-1-111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1111-1-1-111-1-1ii−i−ii−i
χ101111-1-111-11-1-1-111111-111-1-111-1-1-1-111-1-11-1-111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-1-1111-1-111−i−iii−ii
χ111111-1-111-11-1-1-111111-111-1-111-1-1-1-111-1-11-1-111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1111-1-1-111-1-1−i−iii−ii
χ121111-1-111-11-1-1-111111-111-1-111-1-1-1-111-1-11-1-111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-1-1111-1-111ii−i−ii−i
χ131111-1-111-11-1-1-111111-1-1-111-1-111-1-111-1-11-1-111-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii1-111-11-1-1-1-111ii−i−i−ii
χ141111-1-111-11-1-1-111111-1-1-111-1-111-1-111-1-11-1-111-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-11-1-11-11111-1-1−i−iiii−i
χ151111-1-111-11-1-1-111111-1-1-111-1-111-1-111-1-11-1-111-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-111-11-1-1-1-111−i−iiii−i
χ161111-1-111-11-1-1-111111-1-1-111-1-111-1-111-1-11-1-111-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-1-11-11111-1-1ii−i−i−ii
χ172222222222-2-22222-2-2-22222-2-2-2-222-2-2-2-22222-2-22222-2-2-2-20000000000000000000000000000000000
χ182222222222-2-22222-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-222220000000000000000000000000000000000
χ192222222-2-2-222-22222-2-200000000222222-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000
χ202222222-2-2-222-22222-2-200000000222222-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000
χ212222222-2-2-2-2-2-2222-2220000000022-2-2-2-2-2-2-2-222000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ222222222-2-2-2-2-2-2222-2220000000022-2-2-2-2-2-2-2-22200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ23222222-1222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-122-1-1-1-1-1-1000000
χ24222222-1222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-211-2-2111111000000
χ25222222-1222222-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000000022-1-1-2-2-1-11111000000
χ26222222-1222222-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2112211-1-1-1-1000000
χ27222222-1222-2-22-1-1-1-2-2-22222-2-2-2-2-1-11111-1-1-1-111-1-1-1-11111000000000000000000−i3i300−i3i3−i3i3−i3i3000000
χ28222222-1222-2-22-1-1-1-2-2-22222-2-2-2-2-1-11111-1-1-1-111-1-1-1-11111000000000000000000i3−i300i3−i3i3−i3i3−i3000000
χ29222222-1222-2-22-1-1-1-2-2-2-2-2-2-22222-1-11111-1-1-1-1111111-1-1-1-1000000000000000000−i3i300−i3i3i3−i3i3−i3000000
χ30222222-1222-2-22-1-1-1-2-2-2-2-2-2-22222-1-11111-1-1-1-1111111-1-1-1-1000000000000000000i3−i300i3−i3−i3i3−i3i3000000
χ312222-2-222-2222-2222-2-2222-2-2-2-222-2-2-2-2222-2-22-2222-2-2-2-2220000000000000000000000000000000000
χ322222-2-222-2222-2222-2-22-2-22222-2-2-2-2-2-2222-2-22-22-2-22222-2-20000000000000000000000000000000000
χ332222-2-22-22-2222222-22-200000000-2-2-2-222-222-22-20000000022-2-2-2-22200000000000000000000000000
χ342222-2-22-22-2222222-22-200000000-2-2-2-222-222-22-200000000-2-22222-2-200000000000000000000000000
χ352222-2-22-22-2-2-222222-2200000000-2-222-2-2-222-2-2200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ362222-2-22-22-2-2-222222-2200000000-2-222-2-2-222-2-220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ372222-2-2-12-2222-2-1-1-1-2-2222-2-2-2-2221111-1-1-111-11-1-1-11111-1-1000000000000000000−i3i300i3−i3−i3i3i3−i3000000
χ382222-2-2-12-2222-2-1-1-1-2-2222-2-2-2-2221111-1-1-111-11-1-1-11111-1-1000000000000000000i3−i300−i3i3i3−i3−i3i3000000
χ392222-2-2-12-2222-2-1-1-1-2-22-2-22222-2-21111-1-1-111-11-111-1-1-1-111000000000000000000−i3i300i3−i3i3−i3−i3i3000000
χ402222-2-2-12-2222-2-1-1-1-2-22-2-22222-2-21111-1-1-111-11-111-1-1-1-111000000000000000000i3−i300−i3i3−i3i3i3−i3000000
χ412222-2-2-12-22-2-2-2-1-1-122-222-2-222-2-211-1-111-111-1-11-1-111-1-11100000000000000002-2-1-12-211-1-111000000
χ422222-2-2-12-22-2-2-2-1-1-122-222-2-222-2-211-1-111-111-1-11-1-111-1-1110000000000000000-2211-22-1-111-1-1000000
χ432222-2-2-12-22-2-2-2-1-1-122-2-2-222-2-22211-1-111-111-1-1111-1-111-1-100000000000000002-2-1-1-221111-1-1000000
χ442222-2-2-12-22-2-2-2-1-1-122-2-2-222-2-22211-1-111-111-1-1111-1-111-1-10000000000000000-22112-2-1-1-1-111000000
χ452-2-222-222-2-2002-2-220002i−2i2i−2i00002-2000022-2-2002i−2i2i−2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000000000
χ462-2-222-222-2-2002-2-220002i−2i2i−2i00002-2000022-2-2002i−2i2i−2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000000000
χ472-2-222-222-2-2002-2-22000−2i2i−2i2i00002-2000022-2-200−2i2i−2i2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000000000
χ482-2-222-222-2-2002-2-22000−2i2i−2i2i00002-2000022-2-200−2i2i−2i2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000000000
χ492-2-222-22-22200-2-2-2200000002-22-22-20000-2-2220000002-22-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ502-2-222-22-22200-2-2-2200000002-22-22-20000-2-2220000002-22-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ512-2-222-22-22200-2-2-220000000-22-222-20000-2-222000000-22-22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ522-2-222-22-22200-2-2-220000000-22-222-20000-2-222000000-22-22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ532-2-22-22222-200-2-2-220002i−2i−2i2i0000-2200002-22-2002i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000000000
χ542-2-22-22222-200-2-2-220002i−2i−2i2i0000-2200002-22-2002i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000000000
χ552-2-22-22222-200-2-2-22000−2i2i2i−2i0000-2200002-22-200−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000000000
χ562-2-22-22222-200-2-2-22000−2i2i2i−2i0000-2200002-22-200−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000000000
χ572-2-22-222-2-22002-2-2200000002-2-22-220000-22-220000002-2-222−2−22−222−22−2−22−222−2000000000000000000
χ582-2-22-222-2-22002-2-2200000002-2-22-220000-22-220000002-2-22−222−22−2−22−222−22−2−22000000000000000000
χ592-2-22-222-2-22002-2-220000000-222-2-220000-22-22000000-222-22−2−22−222−2−222−22−2−22000000000000000000
χ602-2-22-222-2-22002-2-220000000-222-2-220000-22-22000000-222-2−222−22−2−222−2−22−222−2000000000000000000
χ61444444-2-4-4-444-4-2-2-24-4-400000000-2-2-2-2-2-2222222000000000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-4-2-2-2-44400000000-2-222222222-2-2000000000000000000000000000000000000000000
χ634444-4-4-2-44-4444-2-2-2-44-4000000002222-2-22-2-22-22000000000000000000000000000000000000000000
χ644444-4-4-2-44-4-4-44-2-2-24-440000000022-2-2222-2-222-2000000000000000000000000000000000000000000
χ654-44-40040004i−4i0-44-40000000000000004i−4i0000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ664-44-40040004i−4i0-44-40000000000000004i−4i000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ674-44-4004000−4i4i0-44-4000000000000000−4i4i000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ684-44-4004000−4i4i0-44-4000000000000000−4i4i0000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ694-4-444-4-24-4-400422-20004i−4i4i−4i0000-220000-2-22200−2i2i−2i2i00000000000000000000000000000000000000
χ704-4-444-4-24-4-400422-2000−4i4i−4i4i0000-220000-2-222002i−2i2i−2i00000000000000000000000000000000000000
χ714-4-444-4-2-44400-422-200000004-44-4-22000022-2-2000000-22-220000000000000000000000000000000000
χ724-4-444-4-2-44400-422-20000000-44-44-22000022-2-20000002-22-20000000000000000000000000000000000
χ734-4-44-44-244-400-422-20004i−4i−4i4i00002-20000-22-2200−2i2i2i−2i00000000000000000000000000000000000000
χ744-4-44-44-244-400-422-2000−4i4i4i−4i00002-20000-22-22002i−2i−2i2i00000000000000000000000000000000000000
χ754-4-44-44-2-4-4400422-200000004-4-442-200002-22-2000000-222-20000000000000000000000000000000000
χ764-4-44-44-2-4-4400422-20000000-444-42-200002-22-20000002-2-220000000000000000000000000000000000
χ7788-8-80080000008-8-800000000000000000000000000000000000000000000000000000000000000000
χ7888-8-800-4000000-4440000000000000−4i34i300000000000000000000000000000000000000000000000000
χ7988-8-800-4000000-44400000000000004i3−4i300000000000000000000000000000000000000000000000000
χ808-88-800-40008i−8i04-44000000000000000−4i4i000000000000000000000000000000000000000000000000
χ818-88-800-4000−8i8i04-440000000000000004i−4i000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.