Finite Group Databasebeta

← Group #10768913

Character table — Group #10768913

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881616161616161616161624242424242424242424242424242424
order1222223444466644446612121212121212122444444412121212121212121212688121212242424242244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-111-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1111111-1-1-1-1
χ91111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-111-1-11-11111-1-1-1-111-11-1-111-1-11-1111-111-1-1-1-111-1-1
χ101111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-111-1-11-11111-1-1-1-111-11-1-111-1-1-11-1-1-11-1-11111-1-111
χ111111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-111111-111-1-1-1-1111-1-1-11-111-1-111-1-111
χ121111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-111111-111-1-1-1-111-1111-11-1-111-1-111-1-1
χ131111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-11111-1-11-11111-1-1-1-1-1-11-111-1-1111-1111-1-1-111-1-1-1-111
χ141111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-11111-1-11-11111-1-1-1-1-1-11-111-1-111-11-1-1-1111-1-11111-1-1
χ151111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-111-1-1111-1-1-1-1-11111-11-1-11111-1-11-1-1-11-1-1-1111111-1-1
χ161111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-111-1-1111-1-1-1-1-11111-11-1-11111-1-1-1111-1111-1-1-1-1-1-111
χ17222222222-2-22222-2-2-2222222-2-2-2-200000000-2-20000000000000000002-200-220000000000
χ18222222222-2-22222-2-2-2222222-2-2-2-200000000-2-2000000000000000000-22002-20000000000
χ192222222-2-222222-22-2-222-2-2-2-222-2-200000000-220000000000000000002200-2-20000000000
χ202222222-2-222222-22-2-222-2-2-2-222-2-200000000-22000000000000000000-2-200220000000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-10000000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-2-2-1-1-111110000000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-11-2-211111110000000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111122111-1-1-1-10000000000000000
χ25222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-122-2-222-2-2-11-1-1-1-11111-12-2-111-1-1110000000000000000
χ26222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-122-2-2-2-222-111111-1-1-1-1-1-22-11111-1-10000000000000000
χ27222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-2-22222-2-2-11-1-1-1-111111-221-1-111-1-10000000000000000
χ28222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-2-222-2-222-111111-1-1-1-112-21-1-1-1-1110000000000000000
χ292222-2-222222222-2-2-22-2-222-2-222-2-22-22-200002-200000000200-22-200000000000000000000
χ302222-2-222222222-2-2-22-2-222-2-222-2-2-22-2200002-200000000-2002-2200000000000000000000
χ312222-2-2222-2-2222-222-2-2-222-2-2-2-22200000000-220000000000000000000000002-22-2000000
χ322222-2-2222-2-2222-222-2-2-222-2-2-2-22200000000-22000000000000000000000000-22-22000000
χ332222-2-22-2-2222222-22-2-2-2-2-222222200000000-2-20000000000000000000000002-2-22000000
χ342222-2-22-2-2222222-22-2-2-2-2-222222200000000-2-2000000000000000000000000-222-2000000
χ352222-2-22-2-2-2-222222-22-2-2-2-222-2-2-2-22-2-2200002200000000200-2-2200000000000000000000
χ362222-2-22-2-2-2-222222-22-2-2-2-222-2-2-2-2-222-200002200000000-20022-200000000000000000000
χ372222-2-2-12222-1-1-1-2-2-2211-1-111-1-1112-22-20000-1133−3−333−3−3-1001-113−33−30000000000000000
χ382222-2-2-12222-1-1-1-2-2-2211-1-111-1-1112-22-20000-11−3−333−3−333-1001-11−33−330000000000000000
χ392222-2-2-12222-1-1-1-2-2-2211-1-111-1-111-22-220000-1133−3−333−3−3100-11-1−33−330000000000000000
χ402222-2-2-12222-1-1-1-2-2-2211-1-111-1-111-22-220000-11−3−333−3−333100-11-13−33−30000000000000000
χ412222-2-2-1-2-2-2-2-1-1-122-221111-1-111112-2-220000-1-133−3−3−3−333-10011-13−3−330000000000000000
χ422222-2-2-1-2-2-2-2-1-1-122-221111-1-111112-2-220000-1-1−3−33333−3−3-10011-1−333−30000000000000000
χ432222-2-2-1-2-2-2-2-1-1-122-221111-1-11111-222-20000-1-133−3−3−3−333100-1-11−333−30000000000000000
χ442222-2-2-1-2-2-2-2-1-1-122-221111-1-11111-222-20000-1-1−3−33333−3−3100-1-113−3−330000000000000000
χ45444444-244-4-4-2-2-24-4-4-4-2-2-2-2-2-2222200000000220000000000000000000000000000000000
χ46444444-2-4-444-2-2-2-44-4-4-2-22222-2-222000000002-20000000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-2-444-422-2-22222-2-2000000002-20000000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-24-44-42222-2-2-2-2-2-200000000220000000000000000000000000000000000
χ4944-4-44-4400004-4-400004-400000000000000000000000000000000000000000000000022−2200
χ5044-4-44-4400004-4-400004-4000000000000000000000000000000000000000000000000−222200
χ5144-4-4-44400004-4-40000-4400000000000000000000000000000000000000000000000000−2i22i2
χ5244-4-4-44400004-4-40000-44000000000000000000000000000000000000000000000000002i2−2i2
χ534-44-4004004-4-44-400000000004-40000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ544-44-4004004-4-44-400000000004-4000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ554-44-400400-44-44-40000000000-440000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ564-44-400400-44-44-40000000000-44000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ574-44-400-2004-42-220000000023−23-2223−2300002i−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−ζ2200000000000000000000000000
χ584-44-400-2004-42-220000000023−23-2223−230000−2i2i−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+ζ2200000000000000000000000000
χ594-44-400-2004-42-2200000000−2323-22−232300002i−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−ζ2200000000000000000000000000
χ604-44-400-2004-42-2200000000−2323-22−23230000−2i2i−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+ζ2200000000000000000000000000
χ614-44-400-200-442-220000000023−232-2−232300002i−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+ζ2200000000000000000000000000
χ624-44-400-200-442-220000000023−232-2−23230000−2i2i2i−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−ζ2200000000000000000000000000
χ634-44-400-200-442-2200000000−23232-223−2300002i−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+ζ2200000000000000000000000000
χ644-44-400-200-442-2200000000−23232-223−230000−2i2i2i−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−ζ2200000000000000000000000000
χ654-4-440044i−4i00-4-440000004i−4i0000000000000000000000000000000000002i−2i0000002-20000
χ664-4-440044i−4i00-4-440000004i−4i000000000000000000000000000000000000−2i2i000000-220000
χ674-4-44004−4i4i00-4-44000000−4i4i0000000000000000000000000000000000002i−2i000000-220000
χ684-4-44004−4i4i00-4-44000000−4i4i000000000000000000000000000000000000−2i2i0000002-20000
χ6988-8-88-8-40000-4440000-440000000000000000000000000000000000000000000000000000
χ7088-8-8-88-40000-44400004-40000000000000000000000000000000000000000000000000000
χ718-8-8800-48i−8i0044-4000000−4i4i00000000000000000000000000000000000000000000000000
χ728-8-8800-4−8i8i0044-40000004i−4i00000000000000000000000000000000000000000000000000

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