Finite Group Databasebeta

← Group #10691960

Character table — Group #10691960

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order122222344444466644466888888881212121212121212121224242424242424244444444488888888244466121212121212888888
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
χ5111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111
χ6111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ7111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1
χ8111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111
χ91111-1-111-1-1-11-111111-1-1-1iiii−i−i−i−i-1-111-1-1-1-111iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−iii−i−i1-1
χ101111-1-111-1-1-11-111111-1-1-1iiii−i−i−i−i-1-111-1-1-1-111iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i-11−ii-1-111−i−iii−i−iii-11
χ111111-1-111-1-1-11-111111-1-1-1iiii−i−i−i−i-1-111-1-1-1-111iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii1-1i−i11-1-1ii−i−i−i−iii-11
χ121111-1-111-1-1-11-111111-1-1-1iiii−i−i−i−i-1-111-1-1-1-111iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii-11−ii-1-111−i−iiiii−i−i1-1
χ131111-1-111-1-1-11-111111-1-1-1−i−i−i−iiiii-1-111-1-1-1-111−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii−i−iii1-1
χ141111-1-111-1-1-11-111111-1-1-1−i−i−i−iiiii-1-111-1-1-1-111−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii-11i−i-1-111ii−i−iii−i−i-11
χ151111-1-111-1-1-11-111111-1-1-1−i−i−i−iiiii-1-111-1-1-1-111−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i1-1−ii11-1-1−i−iiiii−i−i-11
χ161111-1-111-1-1-11-111111-1-1-1−i−i−i−iiiii-1-111-1-1-1-111−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i-11i−i-1-111ii−i−i−i−iii1-1
χ17222222222-2-222222-2-2-22200000000-2-22222-2-2-2-2000000002222-2-2-2-200000000000000000000000000
χ18222222222-2-222222-2-2-22200000000-2-22222-2-2-2-200000000-2-2-2-2222200000000000000000000000000
χ192222222-2-222-2-22222-2-22222-2-222-2-2-2-2-2-2-2-2222-222-2-222-2-20000000000000000000000000000000000
χ202222222-2-222-2-22222-2-222-2-222-2-222-2-2-2-2-2-2222-2-2-222-2-2220000000000000000000000000000000000
χ212222222-2-2-2-2-2-2222-222220000000022-2-2-2-2-2-2-2200000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ222222222-2-2-2-2-2-2222-222220000000022-2-2-2-2-2-2-220000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ23222222-1222222-1-1-1222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-1000000
χ24222222-1222222-1-1-1222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-211111111000000
χ25222222-1222222-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-11111000000
χ26222222-1222222-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-1000000
χ27222222-1-2-222-2-2-1-1-12-2-2-1-122-2-222-2-2111111-1-1-11-1-111-1-11100000000000000000000−i3i3−i3i3−i3i3−i3i3000000
χ28222222-1-2-222-2-2-1-1-12-2-2-1-122-2-222-2-2111111-1-1-11-1-111-1-11100000000000000000000i3−i3i3−i3i3−i3i3−i3000000
χ29222222-1-2-222-2-2-1-1-12-2-2-1-1-2-222-2-222111111-1-1-1111-1-111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i3000000
χ30222222-1-2-222-2-2-1-1-12-2-2-1-1-2-222-2-222111111-1-1-1111-1-111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i3000000
χ312222-2-222-2222-2222-2-22-2-2000000002222-2-222-2-20000000022-2-2-2-22200000000000000000000000000
χ322222-2-222-2222-2222-2-22-2-2000000002222-2-222-2-200000000-2-22222-2-200000000000000000000000000
χ332222-2-22-2222-22222-22-2-2-200000000-2-2-2-22222-22000000000000000022-2-2-2-222000000000000000000
χ342222-2-22-2222-22222-22-2-2-200000000-2-2-2-22222-220000000000000000-2-22222-2-2000000000000000000
χ352222-2-22-22-2-2-222222-22-2-22i2i−2i−2i−2i−2i2i2i22-2-222-2-22-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ362222-2-22-22-2-2-222222-22-2-2−2i−2i2i2i2i2i−2i−2i22-2-222-2-22-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ372222-2-2-12-2-2-22-2-1-1-122-2112i2i2i2i−2i−2i−2i−2i11-1-11111-1-1−i−i−i−iiiii00000000000000002-22i−2i-1-111−i−iii000000
χ382222-2-2-12-2-2-22-2-1-1-122-2112i2i2i2i−2i−2i−2i−2i11-1-11111-1-1−i−i−i−iiiii0000000000000000-22−2i2i11-1-1ii−i−i000000
χ392222-2-2-12-2-2-22-2-1-1-122-211−2i−2i−2i−2i2i2i2i2i11-1-11111-1-1iiii−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i000000
χ402222-2-2-12-2-2-22-2-1-1-122-211−2i−2i−2i−2i2i2i2i2i11-1-11111-1-1iiii−i−i−i−i0000000000000000-222i−2i11-1-1−i−iii000000
χ412222-2-2-1-22-2-2-22-1-1-12-22112i2i−2i−2i−2i−2i2i2i-1-111-1-111-11−i−iiiii−i−i00000000000000000000−i3i3i3−i33−3−33000000
χ422222-2-2-1-22-2-2-22-1-1-12-22112i2i−2i−2i−2i−2i2i2i-1-111-1-111-11−i−iiiii−i−i00000000000000000000i3−i3−i3i3−333−3000000
χ432222-2-2-1-22-2-2-22-1-1-12-2211−2i−2i2i2i2i2i−2i−2i-1-111-1-111-11ii−i−i−i−iii00000000000000000000−i3i3i3−i3−333−3000000
χ442222-2-2-1-22-2-2-22-1-1-12-2211−2i−2i2i2i2i2i−2i−2i-1-111-1-111-11ii−i−i−i−iii00000000000000000000i3−i3−i3i33−3−33000000
χ452-2-222-222-200-22-2-220002-2−i2i2−i2i2−i2i2−i2i2002-22-20000−i2i2−i2i2−i2i2−i2i22i−2i2i−2i00002−22−22−22−2000000000000000000
χ462-2-222-222-200-22-2-220002-2−i2i2−i2i2−i2i2−i2i2002-22-20000−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i0000−22−22−22−22000000000000000000
χ472-2-222-222-200-22-2-220002-2i2−i2i2−i2i2−i2i2−i2002-22-20000i2−i2i2−i2i2−i2i2−i22i−2i2i−2i0000−22−22−22−22000000000000000000
χ482-2-222-222-200-22-2-220002-2i2−i2i2−i2i2−i2i2−i2002-22-20000i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i00002−22−22−22−2000000000000000000
χ492-2-222-22-22002-2-2-220002-2−i2i2i2−i2−i2i2i2−i200-22-220000−i2i2i2−i2−i2i2i2−i200002-22-2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ502-2-222-22-22002-2-2-220002-2−i2i2i2−i2−i2i2i2−i200-22-220000−i2i2i2−i2−i2i2i2−i20000-22-22i2−i2−i2i2i2−i2−i2i2000000000000000000
χ512-2-222-22-22002-2-2-220002-2i2−i2−i2i2i2−i2−i2i200-22-220000i2−i2−i2i2i2−i2−i2i200002-22-2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ522-2-222-22-22002-2-2-220002-2i2−i2−i2i2i2−i2−i2i200-22-220000i2−i2−i2i2i2−i2−i2i20000-22-22−i2i2i2−i2−i2i2i2−i2000000000000000000
χ532-2-22-2222200-2-2-2-22000-222−22−2−22−22002-2-2200002−22−2−22−222i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i2000000000000000000
χ542-2-22-2222200-2-2-2-22000-222−22−2−22−22002-2-2200002−22−2−22−22−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i2000000000000000000
χ552-2-22-2222200-2-2-2-22000-22−22−222−22−2002-2-220000−22−222−22−22i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i2000000000000000000
χ562-2-22-2222200-2-2-2-22000-22−22−222−22−2002-2-220000−22−222−22−2−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i2000000000000000000
χ572-2-22-222-2-20022-2-22000-222−2−22−222−200-222-200002−2−22−222−200002-2-222−2−22−222−2000000000000000000
χ582-2-22-222-2-20022-2-22000-222−2−22−222−200-222-200002−2−22−222−20000-222-2−222−22−2−22000000000000000000
χ592-2-22-222-2-20022-2-22000-22−222−22−2−2200-222-20000−222−22−2−2200002-2-22−222−22−2−22000000000000000000
χ602-2-22-222-2-20022-2-22000-22−222−22−2−2200-222-20000−222−22−2−220000-222-22−2−22−222−2000000000000000000
χ61444444-244-4-444-2-2-2-4-4-4-2-20000000022-2-2-2-22222000000000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-4-2-2-2-444-2-200000000-2-22222222-2000000000000000000000000000000000000000000
χ634444-4-4-24-4444-4-2-2-2-4-442200000000-2-2-2-222-2-222000000000000000000000000000000000000000000
χ644444-4-4-2-4444-44-2-2-2-44-422000000002222-2-2-2-22-2000000000000000000000000000000000000000000
χ654-44-4004004i−4i004-4-400000000000000000004i−4i000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ664-44-4004004i−4i004-4-400000000000000000004i−4i00000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ674-44-400400−4i4i004-4-40000000000000000000−4i4i00000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ684-44-400400−4i4i004-4-40000000000000000000−4i4i000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ694-4-444-4-24-400-4422-2000-22−2i22i2−2i22i2−2i22i2−2i22i200-22-220000i2−i2i2−i2i2−i2i2−i20000000000000000000000000000000000
χ704-4-444-4-24-400-4422-2000-222i2−2i22i2−2i22i2−2i22i2−2i200-22-220000−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000
χ714-4-444-4-2-44004-422-2000-22−2i22i22i2−2i2−2i22i22i2−2i2002-22-20000i2−i2−i2i2i2−i2−i2i20000000000000000000000000000000000
χ724-4-444-4-2-44004-422-2000-222i2−2i2−2i22i22i2−2i2−2i22i2002-22-20000−i2i2i2−i2−i2i2i2−i20000000000000000000000000000000000
χ734-4-44-44-24400-4-422-20002-222−2222−22−2222−222200-222-20000−22−222−22−20000000000000000000000000000000000
χ744-4-44-44-24400-4-422-20002-2−2222−222222−2222−2200-222-200002−22−2−22−220000000000000000000000000000000000
χ754-4-44-44-2-4-4004422-20002-222−22−2222−222222−22002-2-220000−222−22−2−220000000000000000000000000000000000
χ764-4-44-44-2-4-4004422-20002-2−222222−2222−22−2222002-2-2200002−2−22−222−20000000000000000000000000000000000
χ7788-8-8008000000-88-800000000000000000000000000000000000000000000000000000000000000000
χ7888-8-800-40000004-44000000000000043−4300000000000000000000000000000000000000000000000000
χ7988-8-800-40000004-440000000000000−434300000000000000000000000000000000000000000000000000
χ808-88-800-4008i−8i00-4440000000000000000000−4i4i00000000000000000000000000000000000000000000
χ818-88-800-400−8i8i00-44400000000000000000004i−4i00000000000000000000000000000000000000000000

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