Finite Group Databasebeta

← Group #10691955

Character table — Group #10691955

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order12222234444446664446688888888121212121212121212122424242424242424222244448888888844881212121224242424888824
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
χ5111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1
χ91111-1-111-11-1-1-11111-11-1-1iiii−i−i−i−i111-1-1-1-111-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−ii−i1-1ii−i−i11-1-1ii−i−i1-1
χ101111-1-111-11-1-1-11111-11-1-1iiii−i−i−i−i111-1-1-1-111-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i−ii-11−i−iii-1-111−i−iii-11
χ111111-1-111-11-1-1-11111-11-1-1iiii−i−i−i−i111-1-1-1-111-1iiii−i−i−i−i-1-111-1-111−i−i−i−iiiiii−i1-1ii−i−i11-1-1−i−iii-11
χ121111-1-111-11-1-1-11111-11-1-1iiii−i−i−i−i111-1-1-1-111-1iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii−ii-11−i−iii-1-111ii−i−i1-1
χ131111-1-111-11-1-1-11111-11-1-1−i−i−i−iiiii111-1-1-1-111-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiiii−i-11ii−i−i-1-111ii−i−i-11
χ141111-1-111-11-1-1-11111-11-1-1−i−i−i−iiiii111-1-1-1-111-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii−ii1-1−i−iii11-1-1−i−iii1-1
χ151111-1-111-11-1-1-11111-11-1-1−i−i−i−iiiii111-1-1-1-111-1−i−i−i−iiiii-1-111-1-111iiii−i−i−i−ii−i-11ii−i−i-1-111−i−iii1-1
χ161111-1-111-11-1-1-11111-11-1-1−i−i−i−iiiii111-1-1-1-111-1−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i−ii1-1−i−iii11-1-1ii−i−i-11
χ172222222222-2-22222-2-2-222000000002-2-222-2-22-2-2000000002222-2-2-2-200000000000000000000000000
χ182222222222-2-22222-2-2-222000000002-2-222-2-22-2-200000000-2-2-2-2222200000000000000000000000000
χ192222222-2-2-222-2222-2-222200000000-2-2-2-2-222-22-2000000000000000022-2-222-2-2000000000000000000
χ202222222-2-2-222-2222-2-222200000000-2-2-2-2-222-22-20000000000000000-2-222-2-222000000000000000000
χ212222222-2-2-2-2-2-222222-2222i2i−2i−2i2i2i−2i−2i-222-2-2-2-2-2-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000
χ222222222-2-2-2-2-2-222222-222−2i−2i2i2i−2i−2i2i2i-222-2-2-2-2-2-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000
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
χ27222222-1-2-2-2-2-2-2-1-1-122-2-1-12i2i−2i−2i2i2i−2i−2i1-1-1111111-1−i−iii−i−iii00000000000000000000−i3i3−i3i33−33−3000000
χ28222222-1-2-2-2-2-2-2-1-1-122-2-1-12i2i−2i−2i2i2i−2i−2i1-1-1111111-1−i−iii−i−iii00000000000000000000i3−i3i3−i3−33−33000000
χ29222222-1-2-2-2-2-2-2-1-1-122-2-1-1−2i−2i2i2i−2i−2i2i2i1-1-1111111-1ii−i−iii−i−i00000000000000000000−i3i3−i3i3−33−33000000
χ30222222-1-2-2-2-2-2-2-1-1-122-2-1-1−2i−2i2i2i−2i−2i2i2i1-1-1111111-1ii−i−iii−i−i00000000000000000000i3−i3i3−i33−33−3000000
χ312222-2-222-2222-2222-22-2-2-2000000002-2-2-2-2222-220000000022-2-2-2-22200000000000000000000000000
χ322222-2-222-2222-2222-22-2-2-2000000002-2-2-2-2222-2200000000-2-22222-2-200000000000000000000000000
χ332222-2-22-22-22222222-2-2-2-222-2-2-2-222-2222222-2-2-222-2-2-2-2220000000000000000000000000000000000
χ342222-2-22-22-22222222-2-2-2-2-2-22222-2-2-2222222-2-2-2-2-22222-2-20000000000000000000000000000000000
χ352222-2-22-22-2-2-22222-222-2-200000000-2-2-222-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ362222-2-22-22-2-2-22222-222-2-200000000-2-2-222-2-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ372222-2-2-12-22-2-2-2-1-1-12-22112i2i2i2i−2i−2i−2i−2i-1-1-11111-1-11−i−i−i−iiiii00000000000000002i−2i2-2−i−iii-1-111000000
χ382222-2-2-12-22-2-2-2-1-1-12-22112i2i2i2i−2i−2i−2i−2i-1-1-11111-1-11−i−i−i−iiiii0000000000000000−2i2i-22ii−i−i11-1-1000000
χ392222-2-2-12-22-2-2-2-1-1-12-2211−2i−2i−2i−2i2i2i2i2i-1-1-11111-1-11iiii−i−i−i−i00000000000000002i−2i-22−i−iii11-1-1000000
χ402222-2-2-12-22-2-2-2-1-1-12-2211−2i−2i−2i−2i2i2i2i2i-1-1-11111-1-11iiii−i−i−i−i0000000000000000−2i2i2-2ii−i−i-1-111000000
χ412222-2-2-1-22-2222-1-1-12-2-21122-2-2-2-2221-1-1-1-1-1-1111-1-11111-1-1000000000000000000003−3−33−333−3000000
χ422222-2-2-1-22-2222-1-1-12-2-21122-2-2-2-2221-1-1-1-1-1-1111-1-11111-1-100000000000000000000−333−33−3−33000000
χ432222-2-2-1-22-2222-1-1-12-2-211-2-22222-2-21-1-1-1-1-1-111111-1-1-1-111000000000000000000003−3−333−3−33000000
χ442222-2-2-1-22-2222-1-1-12-2-211-2-22222-2-21-1-1-1-1-1-111111-1-1-1-11100000000000000000000−333−3−333−3000000
χ452-22-22-222-2-20022-2-20002-22−22−22−22−22002-200-2002−22−22−22−200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000000000000000
χ462-22-22-222-2-20022-2-20002-22−22−22−22−22002-200-2002−22−22−22−20000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000000000000000
χ472-22-22-222-2-20022-2-20002-2−22−22−22−222002-200-200−22−22−22−2200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000000000000000
χ482-22-22-222-2-20022-2-20002-2−22−22−22−222002-200-200−22−22−22−220000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000000000000000
χ492-22-22-22-22200-22-2-20002-2−i2i2i2−i2−i2i2i2−i2-200-2200200−i2i2i2−i2−i2i2i2−i22-22-20000−i2i2i2−i2−i2i2i2−i2000000000000000000
χ502-22-22-22-22200-22-2-20002-2−i2i2i2−i2−i2i2i2−i2-200-2200200−i2i2i2−i2−i2i2i2−i2-22-220000i2−i2−i2i2i2−i2−i2i2000000000000000000
χ512-22-22-22-22200-22-2-20002-2i2−i2−i2i2i2−i2−i2i2-200-2200200i2−i2−i2i2i2−i2−i2i22-22-20000i2−i2−i2i2i2−i2−i2i2000000000000000000
χ522-22-22-22-22200-22-2-20002-2i2−i2−i2i2i2−i2−i2i2-200-2200200i2−i2−i2i2i2−i2−i2i2-22-220000−i2i2i2−i2−i2i2i2−i2000000000000000000
χ532-22-2-22222-200-22-2-2000-22−i2i2−i2i2i2−i2i2−i2200-2200-200−i2i2−i2i2i2−i2i2−i200002i−2i−2i2i−22−222−22−2000000000000000000
χ542-22-2-22222-200-22-2-2000-22−i2i2−i2i2i2−i2i2−i2200-2200-200−i2i2−i2i2i2−i2i2−i20000−2i2i2i−2i2−22−2−22−22000000000000000000
χ552-22-2-22222-200-22-2-2000-22i2−i2i2−i2−i2i2−i2i2200-2200-200i2−i2i2−i2−i2i2−i2i200002i−2i−2i2i2−22−2−22−22000000000000000000
χ562-22-2-22222-200-22-2-2000-22i2−i2i2−i2−i2i2−i2i2200-2200-200i2−i2i2−i2−i2i2−i2i20000−2i2i2i−2i−22−222−22−2000000000000000000
χ572-22-2-222-2-220022-2-2000-222−2−22−222−2-2002-2002002−2−22−222−22-2-2200002−2−22−222−2000000000000000000
χ582-22-2-222-2-220022-2-2000-222−2−22−222−2-2002-2002002−2−22−222−2-222-20000−222−22−2−22000000000000000000
χ592-22-2-222-2-220022-2-2000-22−222−22−2−22-2002-200200−222−22−2−222-2-220000−222−22−2−22000000000000000000
χ602-22-2-222-2-220022-2-2000-22−222−22−2−22-2002-200200−222−22−2−22-222-200002−2−22−222−2000000000000000000
χ61444444-2444-4-44-2-2-2-4-4-4-2-200000000-222-2-222-222000000000000000000000000000000000000000000
χ62444444-2-4-4-444-4-2-2-2-4-44-2-20000000022222-2-22-22000000000000000000000000000000000000000000
χ634444-4-4-24-4444-4-2-2-2-44-42200000000-22222-2-2-22-2000000000000000000000000000000000000000000
χ644444-4-4-2-44-4-4-44-2-2-2-4442200000000222-2-2222-2-2000000000000000000000000000000000000000000
χ6544-4-40040004i−4i0-44-40000000000000000004i−4i0000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ6644-4-40040004i−4i0-44-40000000000000000004i−4i000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ6744-4-4004000−4i4i0-44-4000000000000000000−4i4i000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ6844-4-4004000−4i4i0-44-4000000000000000000−4i4i0000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ694-44-44-4-24-4-4004-222000-2222−2222−2222−2222−22-200-2200200−22−22−22−220000000000000000000000000000000000
χ704-44-44-4-24-4-4004-222000-22−2222−2222−2222−2222-200-22002002−22−22−22−20000000000000000000000000000000000
χ714-44-44-4-2-44400-4-222000-22−2i22i22i2−2i2−2i22i22i2−2i22002-200-200i2−i2−i2i2i2−i2−i2i20000000000000000000000000000000000
χ724-44-44-4-2-44400-4-222000-222i2−2i2−2i22i22i2−2i2−2i22i22002-200-200−i2i2i2−i2−i2i2i2−i20000000000000000000000000000000000
χ734-44-4-44-244-400-4-2220002-2−2i22i2−2i22i22i2−2i22i2−2i2-2002-200200i2−i2i2−i2−i2i2−i2i20000000000000000000000000000000000
χ744-44-4-44-244-400-4-2220002-22i2−2i22i2−2i2−2i22i2−2i22i2-2002-200200−i2i2−i2i2i2−i2i2−i20000000000000000000000000000000000
χ754-44-4-44-2-4-44004-2220002-222−22−2222−222222−22200-2200-200−222−22−2−220000000000000000000000000000000000
χ764-44-4-44-2-4-44004-2220002-2−222222−2222−22−2222200-2200-2002−2−22−222−20000000000000000000000000000000000
χ7788-8-800-40008i−8i04-44000000000000000000−4i4i000000000000000000000000000000000000000000000
χ7888-8-800-4000−8i8i04-440000000000000000004i−4i000000000000000000000000000000000000000000000
χ798-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-400000044-40000000000000043−430000000000000000000000000000000000000000000000000
χ818-8-8800-400000044-400000000000000−43430000000000000000000000000000000000000000000000000

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