Finite Group Databasebeta

← Group #10692549

Character table — Group #10692549

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order12222234444446664446688888888121212121212121212122424242424242424222244448888888844881212121224242424444488
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
χ91111111-1-1-1-1-1-111111-111iiii−i−i−i−i11-1-1-1-1-1-11-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i11-1-1i−i
χ101111111-1-1-1-1-1-111111-111iiii−i−i−i−i11-1-1-1-1-1-11-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-1-111−ii
χ111111111-1-1-1-1-1-111111-111iiii−i−i−i−i11-1-1-1-1-1-11-1iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii1-1i−i11-1-1ii−i−i-1-111−ii
χ121111111-1-1-1-1-1-111111-111iiii−i−i−i−i11-1-1-1-1-1-11-1iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii-11−ii-1-111−i−iii11-1-1i−i
χ131111111-1-1-1-1-1-111111-111−i−i−i−iiiii11-1-1-1-1-1-11-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii11-1-1−ii
χ141111111-1-1-1-1-1-111111-111−i−i−i−iiiii11-1-1-1-1-1-11-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-1-111i−i
χ151111111-1-1-1-1-1-111111-111−i−i−i−iiiii11-1-1-1-1-1-11-1−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i1-1−ii11-1-1−i−iii-1-111i−i
χ161111111-1-1-1-1-1-111111-111−i−i−i−iiiii11-1-1-1-1-1-11-1−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i-11i−i-1-111ii−i−i11-1-1−ii
χ172222222222-2-22222-2-2-22200000000-2-2222-2-22-2-2000000002222-2-2-2-200000000000000000000000000
χ182222222222-2-22222-2-2-22200000000-2-2222-2-22-2-200000000-2-2-2-2222200000000000000000000000000
χ192222222-2-2-222-2222-2-222200000000-2-2-2-2-222-2-220000000022-2-2-2-22200000000000000000000000000
χ202222222-2-2-222-2222-2-222200000000-2-2-2-2-222-2-2200000000-2-22222-2-200000000000000000000000000
χ21222222-1222222-1-1-1222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-1000000
χ22222222-1222222-1-1-1222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-211111111000000
χ23222222-1222222-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-11111000000
χ24222222-1222222-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-1000000
χ25222222-1-2-2-2-2-2-2-1-1-122-2-1-12i2i2i2i−2i−2i−2i−2i-1-1111111-11−i−i−i−iiiii00000000000000002-22i−2i-1-111−i−iii000000
χ26222222-1-2-2-2-2-2-2-1-1-122-2-1-12i2i2i2i−2i−2i−2i−2i-1-1111111-11−i−i−i−iiiii0000000000000000-22−2i2i11-1-1ii−i−i000000
χ27222222-1-2-2-2-2-2-2-1-1-122-2-1-1−2i−2i−2i−2i2i2i2i2i-1-1111111-11iiii−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i000000
χ28222222-1-2-2-2-2-2-2-1-1-122-2-1-1−2i−2i−2i−2i2i2i2i2i-1-1111111-11iiii−i−i−i−i0000000000000000-222i−2i11-1-1−i−iii000000
χ292222-2-222-2222-22222-2-2-2-222-2-222-2-2-2-22-2-22222-222-2-222-2-20000000000000000000000000000000000
χ302222-2-222-2222-22222-2-2-2-2-2-222-2-222-2-22-2-22222-2-2-222-2-2220000000000000000000000000000000000
χ312222-2-222-22-2-2-2222-222-2-200000000222-2-2-2-22-2200000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ322222-2-222-22-2-2-2222-222-2-200000000222-2-2-2-22-220000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ332222-2-22-22-2222222-22-2-2-20000000022-22222-2-2-2000000000000000022-2-2-2-222000000000000000000
χ342222-2-22-22-2222222-22-2-2-20000000022-22222-2-2-20000000000000000-2-22222-2-2000000000000000000
χ352222-2-22-22-2-2-222222-22-2-22i2i−2i−2i−2i−2i2i2i-2-2-222-2-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ362222-2-22-22-2-2-222222-22-2-2−2i−2i2i2i2i2i−2i−2i-2-2-222-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ372222-2-2-12-2222-2-1-1-12-2-21122-2-222-2-211-111-1-1-1-11-1-111-1-11100000000000000000000−i3i3−i3i3−i3i3−i3i3000000
χ382222-2-2-12-2222-2-1-1-12-2-21122-2-222-2-211-111-1-1-1-11-1-111-1-11100000000000000000000i3−i3i3−i3i3−i3i3−i3000000
χ392222-2-2-12-2222-2-1-1-12-2-211-2-222-2-22211-111-1-1-1-1111-1-111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i3000000
χ402222-2-2-12-2222-2-1-1-12-2-211-2-222-2-22211-111-1-1-1-1111-1-111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i3000000
χ412222-2-2-1-22-2-2-22-1-1-12-22112i2i−2i−2i−2i−2i2i2i111-1-1111-1-1−i−iiiii−i−i00000000000000000000−i3i3i3−i33−3−33000000
χ422222-2-2-1-22-2-2-22-1-1-12-22112i2i−2i−2i−2i−2i2i2i111-1-1111-1-1−i−iiiii−i−i00000000000000000000i3−i3−i3i3−333−3000000
χ432222-2-2-1-22-2-2-22-1-1-12-2211−2i−2i2i2i2i2i−2i−2i111-1-1111-1-1ii−i−i−i−iii00000000000000000000−i3i3i3−i3−333−3000000
χ442222-2-2-1-22-2-2-22-1-1-12-2211−2i−2i2i2i2i2i−2i−2i111-1-1111-1-1ii−i−i−i−iii00000000000000000000i3−i3−i3i33−3−33000000
χ452-22-22-222-2-2002-2-220002-2−i2i2−i2i2−i2i2−i2i20022-200-200−i2i2−i2i2−i2i2−i2i200002i−2i2i−2i2−22−22−22−2000000000000000000
χ462-22-22-222-2-2002-2-220002-2−i2i2−i2i2−i2i2−i2i20022-200-200−i2i2−i2i2−i2i2−i2i20000−2i2i−2i2i−22−22−22−22000000000000000000
χ472-22-22-222-2-2002-2-220002-2i2−i2i2−i2i2−i2i2−i20022-200-200i2−i2i2−i2i2−i2i2−i200002i−2i2i−2i−22−22−22−22000000000000000000
χ482-22-22-222-2-2002-2-220002-2i2−i2i2−i2i2−i2i2−i20022-200-200i2−i2i2−i2i2−i2i2−i20000−2i2i−2i2i2−22−22−22−2000000000000000000
χ492-22-22-22-22200-2-2-220002-22−22−2−22−2200-2-22002002−22−2−22−2200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i2000000000000000000
χ502-22-22-22-22200-2-2-220002-22−22−2−22−2200-2-22002002−22−2−22−220000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i2000000000000000000
χ512-22-22-22-22200-2-2-220002-2−22−222−22−200-2-2200200−22−222−22−200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i2000000000000000000
χ522-22-22-22-22200-2-2-220002-2−22−222−22−200-2-2200200−22−222−22−20000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2000000000000000000
χ532-22-2-22222-200-2-2-22000-22−i2i2i2−i2−i2i2i2−i2002-2200-200−i2i2i2−i2−i2i2i2−i22-22-20000−i2i2i2−i2−i2i2i2−i2000000000000000000
χ542-22-2-22222-200-2-2-22000-22−i2i2i2−i2−i2i2i2−i2002-2200-200−i2i2i2−i2−i2i2i2−i2-22-220000i2−i2−i2i2i2−i2−i2i2000000000000000000
χ552-22-2-22222-200-2-2-22000-22i2−i2−i2i2i2−i2−i2i2002-2200-200i2−i2−i2i2i2−i2−i2i22-22-20000i2−i2−i2i2i2−i2−i2i2000000000000000000
χ562-22-2-22222-200-2-2-22000-22i2−i2−i2i2i2−i2−i2i2002-2200-200i2−i2−i2i2i2−i2−i2i2-22-220000−i2i2i2−i2−i2i2i2−i2000000000000000000
χ572-22-2-222-2-22002-2-22000-222−2−22−222−200-22-2002002−2−22−222−22-2-2200002−2−22−222−2000000000000000000
χ582-22-2-222-2-22002-2-22000-222−2−22−222−200-22-2002002−2−22−222−2-222-20000−222−22−2−22000000000000000000
χ592-22-2-222-2-22002-2-22000-22−222−22−2−2200-22-200200−222−22−2−222-2-220000−222−22−2−22000000000000000000
χ602-22-2-222-2-22002-2-22000-22−222−22−2−2200-22-200200−222−22−2−22-222-200002−2−22−222−2000000000000000000
χ61444444-2444-4-44-2-2-2-4-4-4-2-20000000022-2-2-222-222000000000000000000000000000000000000000000
χ62444444-2-4-4-444-4-2-2-2-4-44-2-20000000022222-2-222-2000000000000000000000000000000000000000000
χ634444-4-4-24-44-4-4-4-2-2-2-4442200000000-2-2-22222-22-2000000000000000000000000000000000000000000
χ644444-4-4-2-44-4444-2-2-2-44-42200000000-2-22-2-2-2-2222000000000000000000000000000000000000000000
χ654-44-44-4-24-4-400422-2000-22−2i22i2−2i22i2−2i22i2−2i22i200-2-2200200i2−i2i2−i2i2−i2i2−i20000000000000000000000000000000000
χ664-44-44-4-24-4-400422-2000-222i2−2i22i2−2i22i2−2i22i2−2i200-2-2200200−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000
χ674-44-44-4-2-44400-422-2000-2222−2222−22−2222−22220022-200-200−22−222−22−20000000000000000000000000000000000
χ684-44-44-4-2-44400-422-2000-22−2222−222222−2222−220022-200-2002−22−2−22−220000000000000000000000000000000000
χ694-44-4-44-244-400-422-20002-2−2i22i22i2−2i2−2i22i22i2−2i200-22-200200i2−i2−i2i2i2−i2−i2i20000000000000000000000000000000000
χ704-44-4-44-244-400-422-20002-22i2−2i2−2i22i22i2−2i2−2i22i200-22-200200−i2i2i2−i2−i2i2i2−i20000000000000000000000000000000000
χ714-44-4-44-2-4-4400422-20002-222−22−2222−222222−22002-2200-200−222−22−2−220000000000000000000000000000000000
χ724-44-4-44-2-4-4400422-20002-2−222222−2222−22−2222002-2200-2002−2−22−222−20000000000000000000000000000000000
χ734-4-440040004-404-4-40000000000000000004-40000000000000000000000000000000000000002i−2i2i−2i00
χ744-4-440040004-404-4-40000000000000000004-4000000000000000000000000000000000000000−2i2i−2i2i00
χ754-4-44004000-4404-4-4000000000000000000-440000000000000000000000000000000000000002i−2i−2i2i00
χ764-4-44004000-4404-4-4000000000000000000-44000000000000000000000000000000000000000−2i2i2i−2i00
χ7788-8-8008000000-88-800000000000000000000000000000000000000000000000000000000000000000
χ7888-8-800-40000004-440000000000000−4i34i300000000000000000000000000000000000000000000000000
χ7988-8-800-40000004-4400000000000004i3−4i300000000000000000000000000000000000000000000000000
χ808-8-8800-40008-80-444000000000000000000-44000000000000000000000000000000000000000000000
χ818-8-8800-4000-880-4440000000000000000004-4000000000000000000000000000000000000000000000

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