Finite Group Databasebeta

← Group #10714113

Character table — Group #10714113

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888888888888888888888888888884848484848484848
order1244222344466612121212668888121224242424242424244488121212121616161616161616242424244848484848484848484848484848484822244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-11-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-11-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1
χ922222222222222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2222200000000-2-2-2-2000000000000000000000000
χ1022222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-222-2-2-2-2000000002222000000000000000000000000
χ112222222-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ122222222-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111100000000
χ132222222-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000
χ142222222-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-100000000
χ152222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-10000000011113333−3−3−3−33333−3−3−3−300000000
χ162222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1000000001111−3−3−3−33333−3−3−3−3333300000000
χ172222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-222111100000000-1-1-1-13333−3−3−3−3−3−3−3−3333300000000
χ182222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-222111100000000-1-1-1-1−3−3−3−333333333−3−3−3−300000000
χ1922222-2-22-22-22222222-2-22-22-2-2-222-2-222-2-200000000000022-2-200000000000022-2-222-2-200000000
χ2022222-2-22-22-22222222-2-22-22-2-2-222-2-222-2-2000000000000-2-222000000000000-2-222-2-22200000000
χ2122222-2-22-22-22222222-2-2-22-22-2-2-2-222-2-2220000000022-2-20000000022-2-222-2-20000000000000000
χ2222222-2-22-22-22222222-2-2-22-22-2-2-2-222-2-22200000000-2-22200000000-2-222-2-2220000000000000000
χ2322222-2-2-1-22-2-1-1-1-1-1-1-1112-22-211-1-111-1-111000033−3−3000022-2-233−3−333−3−3−3−333-1-111-1-11100000000
χ2422222-2-2-1-22-2-1-1-1-1-1-1-1112-22-211-1-111-1-111000033−3−30000-2-22233−3−3−3−33333−3−311-1-111-1-100000000
χ2522222-2-2-1-22-2-1-1-1-1-1-1-1112-22-211-1-111-1-1110000−3−333000022-2-2−3−333−3−33333−3−3-1-111-1-11100000000
χ2622222-2-2-1-22-2-1-1-1-1-1-1-1112-22-211-1-111-1-1110000−3−3330000-2-222−3−33333−3−3−3−33311-1-111-1-100000000
χ2722222-2-2-1-22-2-1-1-1-1-1-1-111-22-221111-1-111-1-1000033−3−322-2-20000−3−333-1-111-1-111−3−33333−3−300000000
χ2822222-2-2-1-22-2-1-1-1-1-1-1-111-22-221111-1-111-1-1000033−3−3-2-2220000−3−33311-1-111-1-133−3−3−3−33300000000
χ2922222-2-2-1-22-2-1-1-1-1-1-1-111-22-221111-1-111-1-10000−3−33322-2-2000033−3−3-1-111-1-11133−3−3−3−33300000000
χ3022222-2-2-1-22-2-1-1-1-1-1-1-111-22-221111-1-111-1-10000−3−333-2-222000033−3−311-1-111-1-1−3−33333−3−300000000
χ312222-22-22-2-22-2-2222-2-22-20000-2200000000002-200002−22−22−22−22-22-22−22−22−22−22−22−22−22−200000000
χ322222-22-22-2-22-2-2222-2-22-20000-2200000000002-20000−22−22−22−222-22-2−22−22−22−22−22−22−22−2200000000
χ332222-22-22-2-22-2-2222-2-22-20000-220000000000-2200002−22−2−22−22-22-222−22−22−22−2−22−22−22−2200000000
χ342222-22-22-2-22-2-2222-2-22-20000-220000000000-220000−22−222−22−2-22-22−22−22−22−222−22−22−22−200000000
χ352222-22-2-1-2-2211-1-1-111-1100001-13−33−33−33−3002-23−33−32−22−22−22−2-11-11ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000
χ362222-22-2-1-2-2211-1-1-111-1100001-13−33−33−33−3002-23−33−3−22−22−22−22-11-11−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000
χ372222-22-2-1-2-2211-1-1-111-1100001-13−33−33−33−300-22−33−332−22−2−22−221-11-1ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000
χ382222-22-2-1-2-2211-1-1-111-1100001-13−33−33−33−300-22−33−33−22−222−22−21-11-1−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000
χ392222-22-2-1-2-2211-1-1-111-1100001-1−33−33−33−33002-2−33−332−22−22−22−2-11-11ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000
χ402222-22-2-1-2-2211-1-1-111-1100001-1−33−33−33−33002-2−33−33−22−22−22−22-11-11−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000
χ412222-22-2-1-2-2211-1-1-111-1100001-1−33−33−33−3300-223−33−32−22−2−22−221-11-1ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000
χ422222-22-2-1-2-2211-1-1-111-1100001-1−33−33−33−3300-223−33−3−22−222−22−21-11-1−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000
χ432222-2-2222-2-2-2-2222-2-2-2200002-2000000002-2002-2-222−2−222−2−2200002−2−222−2−222−2−222−2−2200000000
χ442222-2-2222-2-2-2-2222-2-2-2200002-2000000002-2002-2-22−222−2−222−20000−222−2−222−2−222−2−222−200000000
χ452222-2-2222-2-2-2-2222-2-2-2200002-200000000-2200-222-22−2−22−222−200002−2−222−2−22−222−2−222−200000000
χ462222-2-2222-2-2-2-2222-2-2-2200002-200000000-2200-222-2−222−22−2−220000−222−2−222−22−2−222−2−2200000000
χ472222-2-22-12-2-211-1-1-1111-10000-113−3−333−3−332-200-111-12−2−222−2−22−333−3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ482222-2-22-12-2-211-1-1-1111-10000-113−3−333−3−332-200-111-1−222−2−222−2−333−3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ492222-2-22-12-2-211-1-1-1111-10000-113−3−333−3−33-22001-1-112−2−22−222−23−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ502222-2-22-12-2-211-1-1-1111-10000-113−3−333−3−33-22001-1-11−222−22−2−223−3−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ512222-2-22-12-2-211-1-1-1111-10000-11−333−3−333−32-200-111-12−2−222−2−223−3−33ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ522222-2-22-12-2-211-1-1-1111-10000-11−333−3−333−32-200-111-1−222−2−222−23−3−33−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ532222-2-22-12-2-211-1-1-1111-10000-11−333−3−333−3-22001-1-112−2−22−222−2−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ542222-2-22-12-2-211-1-1-1111-10000-11−333−3−333−3-22001-1-11−222−22−2−22−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ5522-2-2-22-2222-2-2-22-2-2222-222-2-22-22222-2-2-2-20000000000000000000000000000000000000000002i−2i
χ5622-2-2-22-2222-2-2-22-2-2222-222-2-22-22222-2-2-2-2000000000000000000000000000000000000000000−2i2i
χ5722-2-2-22-2222-2-2-22-2-2222-2-2-2222-2-2-2-2-2222200000000000000000000000000000000000000200-200
χ5822-2-2-22-2222-2-2-22-2-2222-2-2-2222-2-2-2-2-2222200000000000000000000000000000000000000-200200
χ5922-2-2-2-222-222-2-22-2-222-222-2-22-2222-2-2-2-222000000000000000000000000000000000000200-20000
χ6022-2-2-2-222-222-2-22-2-222-222-2-22-2222-2-2-2-222000000000000000000000000000000000000-20020000
χ6122-2-2-2-222-222-2-22-2-222-22-222-2-22-2-22222-2-20000000000000000000000000000000000000200-2000
χ6222-2-2-2-222-222-2-22-2-222-22-222-2-22-2-22222-2-20000000000000000000000000000000000000-2002000
χ6344-4-44444-4-4-4444-4-4-4-4440000-4-40000000000000000000000000000000000000000000000000000
χ6444-4-4444-2-4-4-4-2-2-22222-2-200002223−2323−23−2323−232300000000000000000000000000000000000000000000
χ6544-4-4444-2-4-4-4-2-2-22222-2-2000022−2323−232323−2323−2300000000000000000000000000000000000000000000
χ6644-4-44-4-444-44444-4-4-4-4-4-40000440000000000000000000000000000000000000000000000000000
χ6744-4-44-4-4-24-44-2-2-22222220000-2-223−23−2323−232323−2300000000000000000000000000000000000000000000
χ6844-4-44-4-4-24-44-2-2-22222220000-2-2−232323−2323−23−232300000000000000000000000000000000000000000000
χ6944-4-4-44-4-244-422-222-2-2-2244-4-4-22-2-2-2-2222200000000000000000000000000000000000000000000
χ7044-4-4-44-4-244-422-222-2-2-22-4-444-222222-2-2-2-200000000000000000000000000000000000000000000
χ7144-4-4-4-44-2-44422-222-2-22-24-4-442-2-2-22222-2-200000000000000000000000000000000000000000000
χ7244-4-4-4-44-2-44422-222-2-22-2-444-42-222-2-2-2-22200000000000000000000000000000000000000000000
χ738-88i−8i000800000-88i−8i00000000000000000000000000000000000000000000000000000000000000
χ748-88i−8i000-4000−4i34i34−4i4i43−43000000000000000000000000000000000000000000000000000000000000
χ758-88i−8i000-40004i3−4i34−4i4i−4343000000000000000000000000000000000000000000000000000000000000
χ768-8−8i8i000800000-8−8i8i00000000000000000000000000000000000000000000000000000000000000
χ778-8−8i8i000-4000−4i34i344i−4i−4343000000000000000000000000000000000000000000000000000000000000
χ788-8−8i8i000-40004i3−4i344i−4i43−43000000000000000000000000000000000000000000000000000000000000

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