Finite Group Databasebeta

← Group #10691940

Character table — Group #10691940

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order12222234444446666666222244444441212121212121212666688881212121212122424242424242424888888888888888844121212124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ711111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ811111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111-1-111-1-11-1-1-1-111-1-1111-1-11-1111-1-111-111-1-1-111-1-1ii−i−i1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−ii−iii−i−i1-11-1
χ101111-1-111-1-11-1-1-1-111-1-1111-1-11-1111-1-111-111-1-1-111-1-1ii−i−i1-111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiii−iii−i−i-11-11
χ111111-1-111-1-11-1-1-1-111-1-1111-1-11-1111-1-111-111-1-1-111-1-1−i−iii1-111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−ii−i−iii-11-11
χ121111-1-111-1-11-1-1-1-111-1-1111-1-11-1111-1-111-111-1-1-111-1-1−i−iii1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−ii−i−iii1-11-1
χ131111-1-111-1-11-1-1-1-111-1-11-1-1111-11-1-11111-111-1-1-1-1-111ii−i−i1-1-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−ii−i−iii1-1-11
χ141111-1-111-1-11-1-1-1-111-1-11-1-1111-11-1-11111-111-1-1-1-1-111ii−i−i1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−ii−i−iii-111-1
χ151111-1-111-1-11-1-1-1-111-1-11-1-1111-11-1-11111-111-1-1-1-1-111−i−iii1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiii−iii−i−i-111-1
χ161111-1-111-1-11-1-1-1-111-1-11-1-1111-11-1-11111-111-1-1-1-1-111−i−iii1-1-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−ii−iii−i−i1-1-11
χ1722222222222-2-222222222222-2-2-2-2-2-2-2222-2-2-2-2222220000-2-2-2-2-2-20000000000000000000000000000000000
χ1822222222222-2-22222222-2-2-2-2-2-2-22222222-2-2-2-22-2-2-2-20000-2-222220000000000000000000000000000000000
χ192222222-2-2-2-22222222220000-2-220000-2-2-22222-200000000-2-20000000000000000000022-2-222-2-20000000000
χ202222222-2-2-2-22222222220000-2-220000-2-2-22222-200000000-2-200000000000000000000-2-222-2-2220000000000
χ212222222-2-2-2-2-2-22222222000022-20000-2-2-2-2-2-2-2-200000000220000000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ222222222-2-2-2-2-2-22222222000022-20000-2-2-2-2-2-2-2-20000000022000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ23222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ24222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111110000000000000000-2-211110000
χ25222222-1222222-1-1-1-1-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-111112222-1-11111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ26222222-1222222-1-1-1-1-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-11111-2-2-2-2-1-1111111111111000000000000000022-1-1-1-10000
χ27222222-12222-2-2-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-10000111111−i3−i3i3i3−i3−i3i3i3000000000000000000−i3i3−i3i30000
χ28222222-12222-2-2-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-10000111111i3i3−i3−i3i3i3−i3−i3000000000000000000i3−i3i3−i30000
χ29222222-12222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-22222-1-1-11111-11111000011-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000i3−i3i3−i30000
χ30222222-12222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-22222-1-1-11111-11111000011-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000−i3i3−i3i30000
χ312222-2-222-2-2222-2-222-2-2222-2-2-22-2-2-22222-2-2-222-222-2-20000-22-2-2220000000000000000000000000000000000
χ322222-2-222-2-2222-2-222-2-22-2-222-22-222-2-222-2-2-222-2-2-2220000-2222-2-20000000000000000000000000000000000
χ332222-2-22-222-222-2-222-2-2200002-2-20000-2-22-2-2222000000002-200000000000022-2-2-2-222000000000000000000
χ342222-2-22-222-222-2-222-2-2200002-2-20000-2-22-2-2222000000002-2000000000000-2-22222-2-2000000000000000000
χ352222-2-22-222-2-2-2-2-222-2-220000-2220000-2-2222-2-2200000000-22000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ362222-2-22-222-2-2-2-2-222-2-220000-2220000-2-2222-2-2200000000-2200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ372222-2-2-12-2-222211-1-111-122-2-2-22-2-2-222-1-1111-1-11-1-11100001-111-1-133−3−3−3−3330000000000000000003−3−330000
χ382222-2-2-12-2-222211-1-111-122-2-2-22-2-2-222-1-1111-1-11-1-11100001-111-1-1−3−33333−3−3000000000000000000−333−30000
χ392222-2-2-12-2-222211-1-111-1-2-222-22-222-2-2-1-1111-1-1111-1-100001-1-1-11133−3−3−3−333000000000000000000−333−30000
χ402222-2-2-12-2-222211-1-111-1-2-222-22-222-2-2-1-1111-1-1111-1-100001-1-1-111−3−33333−3−30000000000000000003−3−330000
χ412222-2-2-12-2-22-2-211-1-111-122-2-22-2222-2-2-1-11-1-1111-1-1112i2i−2i−2i-11-1-111−i−i−i−iiiii00000000000000002i−2i−i−iii0000
χ422222-2-2-12-2-22-2-211-1-111-122-2-22-2222-2-2-1-11-1-1111-1-111−2i−2i2i2i-11-1-111iiii−i−i−i−i0000000000000000−2i2iii−i−i0000
χ432222-2-2-12-2-22-2-211-1-111-1-2-2222-22-2-222-1-11-1-111111-1-12i2i−2i−2i-1111-1-1−i−i−i−iiiii0000000000000000−2i2iii−i−i0000
χ442222-2-2-12-2-22-2-211-1-111-1-2-2222-22-2-222-1-11-1-111111-1-1−2i−2i2i2i-1111-1-1iiii−i−i−i−i00000000000000002i−2i−i−iii0000
χ4522-2-22-2222-2-200222-2-2-2-22-22-200000002-220000-22-22-20000000000000000002−22−22−22−22−22−22−22−20000000000
χ4622-2-22-2222-2-200222-2-2-2-22-22-200000002-220000-22-22-2000000000000000000−22−22−22−22−22−22−22−220000000000
χ4722-2-22-2222-2-200222-2-2-2-2-22-2200000002-220000-2-22-220000000000000000002−22−22−22−2−22−22−22−220000000000
χ4822-2-22-2222-2-200222-2-2-2-2-22-2200000002-220000-2-22-22000000000000000000−22−22−22−222−22−22−22−20000000000
χ4922-2-22-22-2-22200222-2-2-2-200000002i−2i2i−2i-22-20000200000000002i−2i2i−2i00000000−i2i2i2−i2−i2i2i2−i22−2−222−2−220000000000
χ5022-2-22-22-2-22200222-2-2-2-200000002i−2i2i−2i-22-20000200000000002i−2i2i−2i00000000i2−i2−i2i2i2−i2−i2i2−222−2−222−20000000000
χ5122-2-22-22-2-22200222-2-2-2-20000000−2i2i−2i2i-22-2000020000000000−2i2i−2i2i00000000−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000
χ5222-2-22-22-2-22200222-2-2-2-20000000−2i2i−2i2i-22-2000020000000000−2i2i−2i2i00000000i2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000
χ5322-2-2-2222-22-200-2-22-222-22-2-2200000002-2-2000022-2-22000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ5422-2-2-2222-22-200-2-22-222-22-2-2200000002-2-2000022-2-22000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ5522-2-2-2222-22-200-2-22-222-2-222-200000002-2-200002-222-2000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ5622-2-2-2222-22-200-2-22-222-2-222-200000002-2-200002-222-2000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ5722-2-2-222-22-2200-2-22-222-200000002i−2i−2i2i-2220000-200000000002i−2i−2i2i000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i20000000000
χ5822-2-2-222-22-2200-2-22-222-200000002i−2i−2i2i-2220000-200000000002i−2i−2i2i00000000−222−22−2−22−i2i2i2−i2i2−i2−i2i20000000000
χ5922-2-2-222-22-2200-2-22-222-20000000−2i2i2i−2i-2220000-20000000000−2i2i2i−2i000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i20000000000
χ6022-2-2-222-22-2200-2-22-222-20000000−2i2i2i−2i-2220000-20000000000−2i2i2i−2i00000000−222−22−2−22i2−i2−i2i2−i2i2i2−i20000000000
χ61444444-2-4-4-4-444-2-2-2-2-2-2-20000-4-440000222-2-2-2-22000000002200000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-4-2-2-2-2-2-2-2000044-400002222222200000000-2-200000000000000000000000000000000000000
χ634444-4-4-2-444-44422-2-222-200004-4-4000022-222-2-2-200000000-2200000000000000000000000000000000000000
χ644444-4-4-2-444-4-4-422-2-222-20000-444000022-2-2-222-2000000002-200000000000000000000000000000000000000
χ6544-4-44-4-244-4-400-2-2-222224-44-40000000-22-200002-22-2200000000000000000000000000000000000000000000
χ6644-4-44-4-244-4-400-2-2-22222-44-440000000-22-2000022-22-200000000000000000000000000000000000000000000
χ6744-4-44-4-2-4-44400-2-2-2222200000004i−4i4i−4i2-220000-20000000000−2i2i−2i2i0000000000000000000000000000000000
χ6844-4-44-4-2-4-44400-2-2-222220000000−4i4i−4i4i2-220000-200000000002i−2i2i−2i0000000000000000000000000000000000
χ6944-4-4-44-24-44-40022-22-2-224-4-440000000-2220000-2-222-200000000000000000000000000000000000000000000
χ7044-4-4-44-24-44-40022-22-2-22-444-40000000-2220000-22-2-2200000000000000000000000000000000000000000000
χ7144-4-4-44-2-44-440022-22-2-2200000004i−4i−4i4i2-2-2000020000000000−2i2i2i−2i0000000000000000000000000000000000
χ7244-4-4-44-2-44-440022-22-2-220000000−4i4i4i−4i2-2-20000200000000002i−2i−2i2i0000000000000000000000000000000000
χ734-44-400400004i−4i00-4400-400000000000000004i−4i000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000
χ744-44-400400004i−4i00-4400-400000000000000004i−4i00000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000
χ754-44-40040000−4i4i00-4400-40000000000000000−4i4i00000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000
χ764-44-40040000−4i4i00-4400-40000000000000000−4i4i000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000
χ774-44-400-200004i−4i−2i32i32-2−2i32i320000000000000023−23−2i2i000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ2300000000000000000000000000
χ784-44-400-200004i−4i−2i32i32-2−2i32i320000000000000023−23−2i2i00000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ2300000000000000000000000000
χ794-44-400-200004i−4i2i3−2i32-22i3−2i3200000000000000−2323−2i2i000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ2300000000000000000000000000
χ804-44-400-200004i−4i2i3−2i32-22i3−2i3200000000000000−2323−2i2i00000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ2300000000000000000000000000
χ814-44-400-20000−4i4i−2i32i32-2−2i32i3200000000000000−23232i−2i00000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ2300000000000000000000000000
χ824-44-400-20000−4i4i−2i32i32-2−2i32i3200000000000000−23232i−2i000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ2300000000000000000000000000
χ834-44-400-20000−4i4i2i3−2i32-22i3−2i320000000000000023−232i−2i00000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ2300000000000000000000000000
χ844-44-400-20000−4i4i2i3−2i32-22i3−2i320000000000000023−232i−2i000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ2300000000000000000000000000
χ858-8-8800800000000-8-80080000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-4000000−4i34i3444i3−4i3-40000000000000000000000000000000000000000000000000000000000000000000
χ878-8-8800-40000004i3−4i344−4i34i3-40000000000000000000000000000000000000000000000000000000000000000000

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