Finite Group Databasebeta

← Group #10714585

Character table — Group #10714585

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888888888888888888888888888884848484848484848
order1244222344466612121212668888121224242424242424244488121212121616161616161616242424244848484848484848484848484848484822444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1
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
χ1922222-2-22-22-22222222-2-22-22-2-2-222-2-222-2-20000000000002i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i00000000
χ2022222-2-22-22-22222222-2-22-22-2-2-222-2-222-2-2000000000000−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2122222-2-22-22-22222222-2-2-22-22-2-2-2-222-2-222000000002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2222222-2-22-22-22222222-2-2-22-22-2-2-2-222-2-22200000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222-2-2-1-22-2-1-1-1-1-1-1-1112-22-211-1-111-1-111000033−3−300002i2i−2i−2i33−3−3−i3−i3i3i3i3i3−i3−i3−i−iii−i−iii00000000
χ2422222-2-2-1-22-2-1-1-1-1-1-1-1112-22-211-1-111-1-111000033−3−30000−2i−2i2i2i33−3−3i3i3−i3−i3−i3−i3i3i3ii−i−iii−i−i00000000
χ2522222-2-2-1-22-2-1-1-1-1-1-1-1112-22-211-1-111-1-1110000−3−33300002i2i−2i−2i−3−333i3i3−i3−i3−i3−i3i3i3−i−iii−i−iii00000000
χ2622222-2-2-1-22-2-1-1-1-1-1-1-1112-22-211-1-111-1-1110000−3−3330000−2i−2i2i2i−3−333−i3−i3i3i3i3i3−i3−i3ii−i−iii−i−i00000000
χ2722222-2-2-1-22-2-1-1-1-1-1-1-111-22-221111-1-111-1-1000033−3−32i2i−2i−2i0000−3−333−i−iii−i−iiii3i3−i3−i3−i3−i3i3i300000000
χ2822222-2-2-1-22-2-1-1-1-1-1-1-111-22-221111-1-111-1-1000033−3−3−2i−2i2i2i0000−3−333ii−i−iii−i−i−i3−i3i3i3i3i3−i3−i300000000
χ2922222-2-2-1-22-2-1-1-1-1-1-1-111-22-221111-1-111-1-10000−3−3332i2i−2i−2i000033−3−3−i−iii−i−iii−i3−i3i3i3i3i3−i3−i300000000
χ3022222-2-2-1-22-2-1-1-1-1-1-1-111-22-221111-1-111-1-10000−3−333−2i−2i2i2i000033−3−3ii−i−iii−i−ii3i3−i3−i3−i3−i3i3i300000000
χ312222-22-222-2-2-2-2222-2-2-2200002-2000000002-2002-22-2−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ322222-22-222-2-2-2-2222-2-2-2200002-2000000002-2002-22-2i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ332222-22-222-2-2-2-2222-2-2-2200002-200000000-2200-22-22−i2i2−i2i2i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ342222-22-222-2-2-2-2222-2-2-2200002-200000000-2200-22-22i2−i2i2−i2−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ352222-22-2-12-2-211-1-1-1111-10000-113−33−33−33−32-200-11-11−i2i2−i2i2−i2i2−i2i23−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000
χ362222-22-2-12-2-211-1-1-1111-10000-113−33−33−33−32-200-11-11i2−i2i2−i2i2−i2i2−i23−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000
χ372222-22-2-12-2-211-1-1-1111-10000-113−33−33−33−3-22001-11-1−i2i2−i2i2i2−i2i2−i2−33−33ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000
χ382222-22-2-12-2-211-1-1-1111-10000-113−33−33−33−3-22001-11-1i2−i2i2−i2−i2i2−i2i2−33−33−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000
χ392222-22-2-12-2-211-1-1-1111-10000-11−33−33−33−332-200-11-11−i2i2−i2i2−i2i2−i2i2−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000
χ402222-22-2-12-2-211-1-1-1111-10000-11−33−33−33−332-200-11-11i2−i2i2−i2i2−i2i2−i2−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000
χ412222-22-2-12-2-211-1-1-1111-10000-11−33−33−33−33-22001-11-1−i2i2−i2i2i2−i2i2−i23−33−3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000
χ422222-22-2-12-2-211-1-1-1111-10000-11−33−33−33−33-22001-11-1i2−i2i2−i2−i2i2−i2i23−33−3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000
χ432222-2-222-2-22-2-2222-2-22-20000-2200000000002-200002−2−222−2−222-2-222−2−222−2−222−2−222−2−2200000000
χ442222-2-222-2-22-2-2222-2-22-20000-2200000000002-20000−222−2−222−22-2-22−222−2−222−2−222−2−222−200000000
χ452222-2-222-2-22-2-2222-2-22-20000-220000000000-2200002−2−22−222−2-222-22−2−222−2−22−222−2−222−200000000
χ462222-2-222-2-22-2-2222-2-22-20000-220000000000-220000−222−22−2−22-222-2−222−2−222−22−2−222−2−2200000000
χ472222-2-22-1-2-2211-1-1-111-1100001-13−3−333−3−33002-2−333−32−2−222−2−22-111-1ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ482222-2-22-1-2-2211-1-1-111-1100001-13−3−333−3−33002-2−333−3−222−2−222−2-111-1−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ492222-2-22-1-2-2211-1-1-111-1100001-13−3−333−3−3300-223−3−332−2−22−222−21-1-11ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ502222-2-22-1-2-2211-1-1-111-1100001-13−3−333−3−3300-223−3−33−222−22−2−221-1-11−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ512222-2-22-1-2-2211-1-1-111-1100001-1−333−3−333−3002-23−3−332−2−222−2−22-111-1ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ522222-2-22-1-2-2211-1-1-111-1100001-1−333−3−333−3002-23−3−33−222−2−222−2-111-1−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ532222-2-22-1-2-2211-1-1-111-1100001-1−333−3−333−300-22−333−32−2−22−222−21-1-11ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ542222-2-22-1-2-2211-1-1-111-1100001-1−333−3−333−300-22−333−3−222−22−2−221-1-11−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ5522-2-2-22-22-222-2-22-2-222-222-2-22-2222-2-2-2-22200000000000000000000000000000000000020-200000
χ5622-2-2-22-22-222-2-22-2-222-222-2-22-2222-2-2-2-222000000000000000000000000000000000000-20200000
χ5722-2-2-22-22-222-2-22-2-222-22-222-2-22-2-22222-2-2000000000000000000000000000000000000020-20000
χ5822-2-2-22-22-222-2-22-2-222-22-222-2-22-2-22222-2-20000000000000000000000000000000000000-2020000
χ5922-2-2-2-22222-2-2-22-2-2222-222-2-22-22222-2-2-2-20000000000000000000000000000000000000000002i−2i
χ6022-2-2-2-22222-2-2-22-2-2222-222-2-22-22222-2-2-2-2000000000000000000000000000000000000000000−2i2i
χ6122-2-2-2-22222-2-2-22-2-2222-2-2-2222-2-2-2-2-2222200000000000000000000000000000000000000002-200
χ6222-2-2-2-22222-2-2-22-2-2222-2-2-2222-2-2-2-2-222220000000000000000000000000000000000000000-2200
χ6344-4-44444-4-4-4444-4-4-4-4440000-4-40000000000000000000000000000000000000000000000000000
χ6444-4-4444-2-4-4-4-2-2-22222-2-200002223−23−2323−232323−2300000000000000000000000000000000000000000000
χ6544-4-4444-2-4-4-4-2-2-22222-2-2000022−232323−2323−23−232300000000000000000000000000000000000000000000
χ6644-4-44-4-444-44444-4-4-4-4-4-40000440000000000000000000000000000000000000000000000000000
χ6744-4-44-4-4-24-44-2-2-22222220000-2-223−2323−23−2323−232300000000000000000000000000000000000000000000
χ6844-4-44-4-4-24-44-2-2-22222220000-2-2−2323−232323−2323−2300000000000000000000000000000000000000000000
χ6944-4-4-44-4-2-44422-222-2-22-24-4-442-2-2-22222-2-200000000000000000000000000000000000000000000
χ7044-4-4-44-4-2-44422-222-2-22-2-444-42-222-2-2-2-22200000000000000000000000000000000000000000000
χ7144-4-4-4-44-244-422-222-2-2-2244-4-4-22-2-2-2-2222200000000000000000000000000000000000000000000
χ7244-4-4-4-44-244-422-222-2-2-22-4-444-222222-2-2-2-200000000000000000000000000000000000000000000
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.