Finite Group Databasebeta

← Group #10767968

Character table — Group #10767968

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order122222344446664444661212121212121212224444441212121212121212121222226688121224242424224444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1111111-1-1
χ91111111-1-1-1-1111-1-11111-1-1-1-1-1-1111-11-111-1-11-11111-1-1-1-111-1-11-11-11-111-1-11-11-1111-1-1-11-1
χ101111111-1-1-1-1111-1-11111-1-1-1-1-1-1111-11-111-1-11-11111-1-1-1-1-1-1111-11-11-111-1-1-11-11-1-1-1111-11
χ111111111-1-1-1-1111-1-11111-1-1-1-1-1-1111-11-1-1-1111-1-1-1-1-1111111-1-11-1-111-1-1-1111-11-1-1-11-111-11
χ121111111-1-1-1-1111-1-11111-1-1-1-1-1-1111-11-1-1-1111-1-1-1-1-11111-1-1111-1-111-1-1-111-11-1111-11-1-11-1
χ131111111-1-1-1-1111-1-11111-1-1-1-1-1-111-11-1111-1-11-11111-1-1-1-111-1-1-11-11-11-1-111-111-111-11-1-1-11
χ141111111-1-1-1-1111-1-11111-1-1-1-1-1-111-11-1111-1-11-11111-1-1-1-1-1-111-11-11-11-1-1111-1-11-1-11-1111-1
χ151111111-1-1-1-1111-1-11111-1-1-1-1-1-111-11-11-1-1111-1-1-1-1-1111111-1-1-111-1-1111-1-1-111-1-1-1-11111-1
χ161111111-1-1-1-1111-1-11111-1-1-1-1-1-111-11-11-1-1111-1-1-1-1-11111-1-111-111-1-1111-1-11-1-11111-1-1-1-11
χ1722222222222222-2-2-2-2222222-2-2-2-200000000-2-20000000022-2-2000000000000-2200000000
χ1822222222222222-2-2-2-2222222-2-2-2-200000000-2-200000000-2-2220000000000002-200000000
χ192222222-2-2-2-222222-2-222-2-2-2-222-2-200000000-22000000002222000000000000-2-200000000
χ202222222-2-2-2-222222-2-222-2-2-2-222-2-200000000-2200000000-2-2-2-20000000000002200000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000-1-122-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-1-1-2-2-1-11111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1000011-2-2111111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000112211-1-1-1-1000000000000
χ25222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-12-22-222-2-2-11-1-1-1-111110000-112-2-11-1-111000000000000
χ26222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-12-22-2-2-222-111111-1-1-1-10000-11-22-1111-1-1000000000000
χ27222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-22-2222-2-2-11-1-1-1-1111100001-1-221-111-1-1000000000000
χ28222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-22-22-2-222-111111-1-1-1-100001-12-21-1-1-111000000000000
χ292222-2-2222-2-22222-22-2-2-222-2-2222200000000-2-20000000000000000000000220000-2-20000
χ302222-2-2222-2-22222-22-2-2-222-2-2222200000000-2-20000000000000000000000-2-20000220000
χ312222-2-2222-2-2222-22-22-2-222-2-2-2-2-2-222-2-20000220000000000002200-2-20000000000000000
χ322222-2-2222-2-2222-22-22-2-222-2-2-2-2-2-2-2-222000022000000000000-2-200220000000000000000
χ332222-2-22-2-2222222-2-22-2-2-2-22222-2-22-2-2200002-20000000000002-200-220000000000000000
χ342222-2-22-2-2222222-2-22-2-2-2-22222-2-2-222-200002-2000000000000-22002-20000000000000000
χ352222-2-22-2-222222-222-2-2-2-2-222-2-22200000000-2200000000000000000000002-20000-220000
χ362222-2-22-2-222222-222-2-2-2-2-222-2-22200000000-220000000000000000000000-2200002-20000
χ372222-2-2-122-2-2-1-1-1-22-2211-1-111111122-2-20000-1-133−3−333−3−30000-1-100113−33−3000000000000
χ382222-2-2-122-2-2-1-1-1-22-2211-1-111111122-2-20000-1-1−3−333−3−3330000-1-10011−33−33000000000000
χ392222-2-2-122-2-2-1-1-1-22-2211-1-1111111-2-2220000-1-133−3−333−3−300001100-1-1−33−33000000000000
χ402222-2-2-122-2-2-1-1-1-22-2211-1-1111111-2-2220000-1-1−3−333−3−33300001100-1-13−33−3000000000000
χ412222-2-2-1-2-222-1-1-12-2-221111-1-1-1-1112-2-220000-1133−3−3−3−3330000-11001-13−3−33000000000000
χ422222-2-2-1-2-222-1-1-12-2-221111-1-1-1-1112-2-220000-11−3−33333−3−30000-11001-1−333−3000000000000
χ432222-2-2-1-2-222-1-1-12-2-221111-1-1-1-111-222-20000-1133−3−3−3−33300001-100-11−333−3000000000000
χ442222-2-2-1-2-222-1-1-12-2-221111-1-1-1-111-222-20000-11−3−33333−3−300001-100-113−3−33000000000000
χ45444444-24444-2-2-2-4-4-4-4-2-2-2-2-2-2222200000000220000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-244-4-4-2-22222-2-222000000002-20000000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-24-44-422-2-222-2-2-2-200000000220000000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-2-444-42222-2-222-2-2000000002-20000000000000000000000000000000000
χ4944-4-4004004i−4i4-4-4000000004i−4i00000000000000000000000000000000000000002-2002i−2i00
χ5044-4-4004004i−4i4-4-4000000004i−4i0000000000000000000000000000000000000000-2200−2i2i00
χ5144-4-400400−4i4i4-4-400000000−4i4i00000000000000000000000000000000000000002-200−2i2i00
χ5244-4-400400−4i4i4-4-400000000−4i4i0000000000000000000000000000000000000000-22002i−2i00
χ534-44-40044-400-44-40000004-400000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ544-44-40044-400-44-40000004-40000000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ554-44-4004-4400-44-4000000-4400000000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ564-44-4004-4400-44-4000000-440000000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ574-44-400-24-4002-22000000-220023−2323−2300002i−2i2i−2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000000
χ584-44-400-24-4002-22000000-220023−2323−230000−2i2i−2i2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000000
χ594-44-400-24-4002-22000000-2200−2323−232300002i−2i2i−2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000000
χ604-44-400-24-4002-22000000-2200−2323−23230000−2i2i−2i2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000000
χ614-44-400-2-44002-220000002-20023−23−232300002i−2i−2i2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000000
χ624-44-400-2-44002-220000002-20023−23−23230000−2i2i2i−2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000000
χ634-44-400-2-44002-220000002-200−232323−2300002i−2i−2i2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000000
χ644-44-400-2-44002-220000002-200−232323−230000−2i2i2i−2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000000
χ654-4-444-440000-4-4400004-400000000000000000000000000004-40000000000000000000000
χ664-4-444-440000-4-4400004-40000000000000000000000000000-440000000000000000000000
χ674-4-44-4440000-4-440000-44000000000000000000000000004-4000000000000000000000000
χ684-4-44-4440000-4-440000-4400000000000000000000000000-44000000000000000000000000
χ6988-8-800-4008i−8i-44400000000−4i4i000000000000000000000000000000000000000000000000
χ7088-8-800-400−8i8i-444000000004i−4i000000000000000000000000000000000000000000000000
χ718-8-888-8-4000044-40000-440000000000000000000000000000000000000000000000000000
χ728-8-88-88-4000044-400004-40000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.