Finite Group Databasebeta

← Group #10770431

Character table — Group #10770431

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888161616161616161616162424242424242424242424244848
order12222234466644444661212121212121212444444441212121212121212121288121212122424242424444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-111111-1-1
χ6111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11-1-11-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-111-11111-1-1
χ91111111-1-1111-1-1-11111-1-1-1-1-1-1111-11-111-1-1-111111-1-1-1-11-111-1-111-1-1111-1-11-1-111-1-11-1
χ101111111-1-1111-1-1-11111-1-1-1-1-1-1111-11-111-1-1-111111-1-1-1-11-111-1-111-1-1-1-1-111-111-1-111-11
χ111111111-1-1111-1-1-11111-1-1-1-1-1-1111-11-1-1-111-11-1-1-1-11111-1111-1-1-1-111111-1-11-1-1-1-111-11
χ121111111-1-1111-1-1-11111-1-1-1-1-1-1111-11-1-1-111-11-1-1-1-11111-1111-1-1-1-111-1-1-111-11111-1-11-1
χ131111111-1-1111-1-1-11111-1-1-1-1-1-111-11-1111-1-1-111111-1-1-1-1-11-1-111-1-11111-11-1-11-111-1-1-11
χ141111111-1-1111-1-1-11111-1-1-1-1-1-111-11-1111-1-1-111111-1-1-1-1-11-1-111-1-111-1-11-111-11-1-1111-1
χ151111111-1-1111-1-1-11111-1-1-1-1-1-111-11-11-1-111-11-1-1-1-111111-1-1-11111-1-111-11-1-11-1-1-1111-1
χ161111111-1-1111-1-1-11111-1-1-1-1-1-111-11-11-1-111-11-1-1-1-111111-1-1-11111-1-1-1-11-111-1111-1-1-11
χ17222222222222-2-22-2-222-2-22222-2-200000000-2-200000000000000000000220-2-20000000
χ18222222222222-2-22-2-222-2-22222-2-200000000-2-200000000000000000000-2-20220000000
χ192222222-2-222222-2-2-22222-2-2-2-2-2-2000000002-2000000000000000000002-20-220000000
χ202222222-2-222222-2-2-22222-2-2-2-2-2-2000000002-200000000000000000000-2202-20000000
χ21222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000
χ22222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-2-2-1-1-1-1111100000000000000
χ23222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-2-21111111100000000000000
χ24222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111221111-1-1-1-100000000000000
χ25222222-1-2-2-1-1-1-2-2-222-1-1111111-1-12-22-222-2-21-1-1-1-1-111112-2-1-111-1-11100000000000000
χ26222222-1-2-2-1-1-1-2-2-222-1-1111111-1-12-22-2-2-2221-11111-1-1-1-1-22-1-11111-1-100000000000000
χ27222222-1-2-2-1-1-1-2-2-222-1-1111111-1-1-22-2222-2-21-1-1-1-1-11111-2211-1-111-1-100000000000000
χ28222222-1-2-2-1-1-1-2-2-222-1-1111111-1-1-22-22-2-2221-11111-1-1-1-12-211-1-1-1-11100000000000000
χ292222-2-22222222-2-22-2-2-22222-2-22200000000-2-20000000000000000002-200-2002000000
χ302222-2-22222222-2-22-2-2-22222-2-22200000000-2-2000000000000000000-2200200-2000000
χ312222-2-2222222-22-2-22-2-2-2-222-2-2-2-222-2-200002200000000002-22-2000000000000000000
χ322222-2-2222222-22-2-22-2-2-2-222-2-2-2-2-2-2220000220000000000-22-22000000000000000000
χ332222-2-22-2-22222-22-22-2-222-2-222-2-22-2-220000-2200000000002-2-22000000000000000000
χ342222-2-22-2-22222-22-22-2-222-2-222-2-2-222-20000-220000000000-222-2000000000000000000
χ352222-2-22-2-2222-2222-2-2-2-2-2-2-22222000000002-20000000000000000002-200200-2000000
χ362222-2-22-2-2222-2222-2-2-2-2-2-2-22222000000002-2000000000000000000-2200-2002000000
χ372222-2-2-122-1-1-1-22-2-221111-1-1111122-2-20000-1-133−3−333−3−300-11-113−33−300000000000000
χ382222-2-2-122-1-1-1-22-2-221111-1-1111122-2-20000-1-1−3−333−3−33300-11-11−33−3300000000000000
χ392222-2-2-122-1-1-1-22-2-221111-1-11111-2-2220000-1-133−3−333−3−3001-11-1−33−3300000000000000
χ402222-2-2-122-1-1-1-22-2-221111-1-11111-2-2220000-1-1−3−333−3−333001-11-13−33−300000000000000
χ412222-2-2-1-2-2-1-1-12-22-2211-1-111-1-1112-2-2200001-133−3−3−3−33300-111-13−3−3300000000000000
χ422222-2-2-1-2-2-1-1-12-22-2211-1-111-1-1112-2-2200001-1−3−33333−3−300-111-1−333−300000000000000
χ432222-2-2-1-2-2-1-1-12-22-2211-1-111-1-111-222-200001-133−3−3−3−333001-1-11−333−300000000000000
χ442222-2-2-1-2-2-1-1-12-22-2211-1-111-1-111-222-200001-1−3−33333−3−3001-1-113−3−3300000000000000
χ45444444-244-2-2-2-4-44-4-4-2-222-2-2-2-222000000002200000000000000000000000000000000
χ46444444-2-4-4-2-2-244-4-4-4-2-2-2-222222200000000-2200000000000000000000000000000000
χ474444-4-4-244-2-2-24-4-44-422-2-2-2-222-2-2000000002200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-2-4444-4222222-2-2-2-200000000-2200000000000000000000000000000000
χ4944-4-44-44004-4-4000004-40000000000000000000000000000000000000000000022−220000
χ5044-4-44-44004-4-4000004-400000000000000000000000000000000000000000000−22220000
χ5144-4-4-444004-4-400000-44000000000000000000000000000000000000000000000022−2200
χ5244-4-4-444004-4-400000-440000000000000000000000000000000000000000000000−222200
χ534-4-440044-4-44-40000000004-4000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ544-4-440044-4-44-40000000004-400000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ554-4-44004-44-44-4000000000-44000000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ564-4-44004-44-44-4000000000-4400000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ574-4-4400-24-42-22000000023−23-220023−2300002i−2i2i−2i00−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000
χ584-4-4400-24-42-22000000023−23-220023−230000−2i2i−2i2i00ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000
χ594-4-4400-24-42-220000000−2323-2200−232300002i−2i2i−2i00ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000
χ604-4-4400-24-42-220000000−2323-2200−23230000−2i2i−2i2i00−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000
χ614-4-4400-2-442-22000000023−232-200−232300002i−2i−2i2i00ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000
χ624-4-4400-2-442-22000000023−232-200−23230000−2i2i2i−2i00−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000
χ634-4-4400-2-442-220000000−23232-20023−2300002i−2i−2i2i00−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000
χ644-4-4400-2-442-220000000−23232-20023−230000−2i2i2i−2i00ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000
χ6588-8-88-8-400-44400000-4400000000000000000000000000000000000000000000000000
χ6688-8-8-88-400-444000004-400000000000000000000000000000000000000000000000000
χ678-88-800800-8-88000000000000000000000000000000000000000000000000000000000
χ688-88-800-40044-40000000000043−4300000000000000000000000000000000000000000000
χ698-88-800-40044-400000000000−434300000000000000000000000000000000000000000000

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