Finite Group Databasebeta

← Group #10773109

Character table — Group #10773109

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444444444444444444444444888816161616161616161616242424242424242448484848
order1222223444466612121212444466888888881212121212121212121224242424242424242424242424242424244468812121224242424244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111111-1-1-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111-1-111
χ91111-1-1111111111111-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-11-1-111-1-111-1-111-1-11-11-1
χ101111-1-1111111111111-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-11-1-111-1-1-1-111-1-111-11-11
χ111111-1-1111111111111-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-11-111-1-11111-1-1-1-111-111-1
χ121111-1-1111111111111-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-11-111-1-111-1-11111-1-11-1-11
χ131111-1-1111111111111-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-11-111-1-1-1-11111-1-111-1-1-11-11
χ141111-1-1111111111111-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-11-111-1-1-1-111-1-111-1-1111-11-1
χ151111-1-1111111111111-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-11-11-1-11111-1-111-1-1-1-1111-1-11
χ161111-1-1111111111111-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-11-11-1-11111-1-1-1-11111-1-1-111-1
χ17222222222-2-22222222-22-2-22200000000-2-222-2-2-2-2-2-20000000000000000000000000000002-22-200000000
χ18222222222-2-22222222-22-2-22200000000-2-222-2-2-2-2-2-2000000000000000000000000000000-22-2200000000
χ192222222-2-222222-2-2-2-22-2-2-2220000000022-2-222-2-2-2-200000000000000002-2-22200-22-20000000000000000
χ202222222-2-222222-2-2-2-22-2-2-2220000000022-2-222-2-2-2-20000000000000000-222-2-2002-220000000000000000
χ212222222-2-2-2-2222-2-2-2-2-2-2222200000000-2-2-2-2-2-2222200000000000000000000000000000000002-22-20000
χ222222222-2-2-2-2222-2-2-2-2-2-2222200000000-2-2-2-2-2-222220000000000000000000000000000000000-22-220000
χ23222222-12222-1-1-1-1-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-122-1-1-1-1-1-1-1000000000000
χ24222222-12222-1-1-1-1-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21-2-21111111000000000000
χ25222222-12222-1-1-1-1-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111112222-1-2-2-1-1-11111000000000000
χ26222222-12222-1-1-1-1-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-2122111-1-1-1-1000000000000
χ27222222-1-2-222-1-1-111112-2-2-2-1-100000000-1-111-1-111113333−3−3−3−33333−3−3−3−32-2-22-1001-113−33−3000000000000
χ28222222-1-2-222-1-1-111112-2-2-2-1-100000000-1-111-1-111113333−3−3−3−33333−3−3−3−3-222-2100-11-1−33−33000000000000
χ29222222-1-2-222-1-1-111112-2-2-2-1-100000000-1-111-1-11111−3−3−3−33333−3−3−3−333332-2-22-1001-11−33−33000000000000
χ30222222-1-2-222-1-1-111112-2-2-2-1-100000000-1-111-1-11111−3−3−3−33333−3−3−3−33333-222-2100-11-13−33−3000000000000
χ312222-2-2222-2-222222222-22-2-2-200000000-2-2-2-22222-2-20000000000000000000000000000002-2-2200000000
χ322222-2-2222-2-222222222-22-2-2-200000000-2-2-2-22222-2-2000000000000000000000000000000-222-200000000
χ332222-2-22-2-222222-2-2-2-2-222-2-2-2000000002222-2-222-2-2000000000000000022-2-2200-2-220000000000000000
χ342222-2-22-2-222222-2-2-2-2-222-2-2-2000000002222-2-222-2-20000000000000000-2-222-20022-20000000000000000
χ352222-2-22-2-2-2-2222-2-2-2-222-22-2-200000000-2-22222-2-22200000000000000000000000000000000002-2-220000
χ362222-2-22-2-2-2-2222-2-2-2-222-22-2-200000000-2-22222-2-2220000000000000000000000000000000000-222-20000
χ372222-2-2-12222-1-1-1-1-1-1-1-2-2-22112222-2-2-2-2-1-1111111-1-1-1-1-1-1-1-1-1-1111111112-22-2-12-2-111-1-111000000000000
χ382222-2-2-12222-1-1-1-1-1-1-1-2-2-22112222-2-2-2-2-1-1111111-1-1-1-1-1-1-1-1-1-111111111-22-221-221-1-111-1-1000000000000
χ392222-2-2-12222-1-1-1-1-1-1-1-2-2-2211-2-2-2-22222-1-1111111-1-111111111-1-1-1-1-1-1-1-12-22-2-1-22-11111-1-1000000000000
χ402222-2-2-12222-1-1-1-1-1-1-1-2-2-2211-2-2-2-22222-1-1111111-1-111111111-1-1-1-1-1-1-1-1-22-2212-21-1-1-1-111000000000000
χ412222-2-2-1-2-222-1-1-11111-222-21100000000-1-1-1-111-1-1113333−3−3−3−3−3−3−3−3333322-2-2-10011-13−3−33000000000000
χ422222-2-2-1-2-222-1-1-11111-222-21100000000-1-1-1-111-1-1113333−3−3−3−3−3−3−3−33333-2-222100-1-11−333−3000000000000
χ432222-2-2-1-2-222-1-1-11111-222-21100000000-1-1-1-111-1-111−3−3−3−333333333−3−3−3−322-2-2-10011-1−333−3000000000000
χ442222-2-2-1-2-222-1-1-11111-222-21100000000-1-1-1-111-1-111−3−3−3−333333333−3−3−3−3-2-222100-1-113−3−33000000000000
χ45444444-244-4-4-2-2-2-2-2-2-2-44-4-4-2-20000000022-2-2222222000000000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-22222-4-444-2-200000000222222-2-2-2-2000000000000000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-2-2-2-2-24-44-422000000002222-2-2-2-222000000000000000000000000000000000000000000
χ484444-4-4-2-4-4-4-4-2-2-2222244-44220000000022-2-2-2-222-2-2000000000000000000000000000000000000000000
χ4944-4-4004004-44-4-4000000000000002222−22−224-400000000000000002222−22−222222−22−2200000000000000000000000000
χ5044-4-4004004-44-4-400000000000000−22−2222224-40000000000000000−22−222222−22−22222200000000000000000000000000
χ5144-4-400400-444-4-400000000002222−22−220000-44000000002222−22−222222−22−220000000000000000000000000000000000
χ5244-4-400400-444-4-40000000000−22−2222220000-4400000000−22−222222−22−2222220000000000000000000000000000000000
χ5344-4-400-2004-4-2222323−23−2300000000002222−22−22-2200000023−23000000002ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ700000000000000000000000000
χ5444-4-400-2004-4-2222323−23−230000000000−22−222222-2200000023−2300000000−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ700000000000000000000000000
χ5544-4-400-2004-4-222−23−23232300000000002222−22−22-22000000−2323000000002ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ2300000000000000000000000000
χ5644-4-400-2004-4-222−23−2323230000000000−22−222222-22000000−232300000000−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ2300000000000000000000000000
χ5744-4-400-200-44-2222323−23−230000002222−22−2200002-2000000−23232ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ230000000000000000000000000000000000
χ5844-4-400-200-44-2222323−23−23000000−22−22222200002-2000000−2323−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ230000000000000000000000000000000000
χ5944-4-400-200-44-222−23−2323230000002222−22−2200002-200000023−232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ70000000000000000000000000000000000
χ6044-4-400-200-44-222−23−232323000000−22−22222200002-200000023−23−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ70000000000000000000000000000000000
χ614-44-40044-400-44-44-44-40000000000−2i22i2−2i22i2000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000
χ624-44-40044-400-44-44-44-400000000002i2−2i22i2−2i20000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000
χ634-44-4004-4400-44-4-44-44000000−2i22i2−2i22i200000000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000000000
χ644-44-4004-4400-44-4-44-440000002i2−2i22i2−2i2000000000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000000000
χ654-44-400-24-4002-22-22-220000000000−2i22i2−2i22i2000023−2323−2300i6−i6i6−i6−i6i6−i6i6i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ664-44-400-24-4002-22-22-220000000000−2i22i2−2i22i20000−2323−232300−i6i6−i6i6i6−i6i6−i6i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ674-44-400-24-4002-22-22-2200000000002i2−2i22i2−2i2000023−2323−2300−i6i6−i6i6i6−i6i6−i6−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ684-44-400-24-4002-22-22-2200000000002i2−2i22i2−2i20000−2323−232300i6−i6i6−i6−i6i6−i6i6−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ694-44-400-2-44002-222-22-2000000−2i22i2−2i22i20000000023−23−232300i2−i2i2−i2i2−i2i2−i2−i6i6−i6i6i6−i6i6−i600000000000000000000000000
χ704-44-400-2-44002-222-22-2000000−2i22i2−2i22i200000000−232323−2300i2−i2i2−i2i2−i2i2−i2i6−i6i6−i6−i6i6−i6i600000000000000000000000000
χ714-44-400-2-44002-222-22-20000002i2−2i22i2−2i20000000023−23−232300−i2i2−i2i2−i2i2−i2i2i6−i6i6−i6−i6i6−i6i600000000000000000000000000
χ724-44-400-2-44002-222-22-20000002i2−2i22i2−2i200000000−232323−2300−i2i2−i2i2−i2i2−i2i2−i6i6−i6i6i6−i6i6−i600000000000000000000000000
χ734-4-444-440000-4-44000000004-42i−2i−2i2i2i−2i−2i2i00000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ744-4-444-440000-4-44000000004-4−2i2i2i−2i−2i2i2i−2i0000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ754-4-444-4-2000022-223−23−23230000-222i−2i−2i2i2i−2i−2i2i0023−23000000−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+ζ22−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
χ764-4-444-4-2000022-223−23−23230000-22−2i2i2i−2i−2i2i2i−2i0023−23000000ζ4−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−ζ22ζ4−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
χ774-4-444-4-2000022-2−232323−230000-222i−2i−2i2i2i−2i−2i2i00−2323000000ζ4+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+ζ22ζ4+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
χ784-4-444-4-2000022-2−232323−230000-22−2i2i2i−2i−2i2i2i−2i00−2323000000−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−ζ22−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
χ794-4-44-4440000-4-4400000000-442i−2i−2i2i−2i2i2i−2i00000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ804-4-44-4440000-4-4400000000-44−2i2i2i−2i2i−2i−2i2i0000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ814-4-44-44-2000022-223−23−232300002-22i−2i−2i2i−2i2i2i−2i00−2323000000−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+ζ22ζ4−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
χ824-4-44-44-2000022-223−23−232300002-2−2i2i2i−2i2i−2i−2i2i00−2323000000ζ4−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−ζ22−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
χ834-4-44-44-2000022-2−232323−2300002-22i−2i−2i2i−2i2i2i−2i0023−23000000ζ4+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+ζ22−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
χ844-4-44-44-2000022-2−232323−2300002-2−2i2i2i−2i2i−2i−2i2i0023−23000000−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−ζ22ζ4+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

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