Finite Group Databasebeta

← Group #10691697

Character table — Group #10691697

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222224444444444444444444444444444444444488888888888888888888888888242424242424242448484848
order12222234444446661212121244466888888881212121212122424242424242424242424242424242444448888121212121212121212122424242424242424888888884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ61111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ91111111-1-1-1-1-1-1111-1-1-1-1-11111ii−i−iii−i−i-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i1-11111-1-1-1-1ii−i−iii−i−iii−i−i11-1-11-1i−i
χ101111111-1-1-1-1-1-1111-1-1-1-1-11111ii−i−iii−i−i-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i1-11111-1-1-1-1ii−i−iii−i−i−i−iii-1-111-11−ii
χ111111111-1-1-1-1-1-1111-1-1-1-1-11111ii−i−i−i−iii-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-11i−i−ii1-1-1-1-1-11111ii−i−i−i−iiiii−i−i11-1-1-11−ii
χ121111111-1-1-1-1-1-1111-1-1-1-1-11111ii−i−i−i−iii-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-11i−i−ii1-1-1-1-1-11111ii−i−i−i−iii−i−iii-1-1111-1i−i
χ131111111-1-1-1-1-1-1111-1-1-1-1-11111−i−iiiii−i−i-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-11−iii−i1-1-1-1-1-11111−i−iiiii−i−iii−i−i-1-1111-1−ii
χ141111111-1-1-1-1-1-1111-1-1-1-1-11111−i−iiiii−i−i-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-11−iii−i1-1-1-1-1-11111−i−iiiii−i−i−i−iii11-1-1-11i−i
χ151111111-1-1-1-1-1-1111-1-1-1-1-11111−i−iii−i−iii-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii1-11111-1-1-1-1−i−iii−i−iiiii−i−i-1-111-11i−i
χ161111111-1-1-1-1-1-1111-1-1-1-1-11111−i−iii−i−iii-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii1-11111-1-1-1-1−i−iii−i−iii−i−iii11-1-11-1−ii
χ1722222222-2222-22222222-2-2-2222222000022-2-2-2-222222222000000000000-2-200-2-200000000-2-2-2-20000000000000000
χ1822222222-2222-22222222-2-2-222-2-2-2-2000022-2-2-2-2-2-2-2-2-2-2-2-20000000000002200-2-20000000022220000000000000000
χ192222222-22-2-2-22222-2-2-2-22-2-2222i2i−2i−2i0000-2-2-2-2222i2i2i2i−2i−2i−2i−2i000000000000−2i2i00-2200000000−2i−2i2i2i0000000000000000
χ202222222-22-2-2-22222-2-2-2-22-2-222−2i−2i2i2i0000-2-2-2-222−2i−2i−2i−2i2i2i2i2i0000000000002i−2i00-22000000002i2i−2i−2i0000000000000000
χ21222222-1222222-1-1-1-1-1-1-1222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-1222-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-222-2-2-1-111111111-1-1-1-11111000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-22222-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1111111111111-1-1-1-1000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000
χ25222222-12-2222-2-1-1-1-1-1-1-1-2-2-2-1-122220000-1-11111-1-1-1-1-1-1-1-1−i3−i3i3i3−i3−i3i3i30000-2-20011−i3−i3i3i3−i3−i3i3i31111−i3i3−i3i3000000000000
χ26222222-12-2222-2-1-1-1-1-1-1-1-2-2-2-1-122220000-1-11111-1-1-1-1-1-1-1-1i3i3−i3−i3i3i3−i3−i30000-2-20011i3i3−i3−i3i3i3−i3−i31111i3−i3i3−i3000000000000
χ27222222-12-2222-2-1-1-1-1-1-1-1-2-2-2-1-1-2-2-2-20000-1-1111111111111−i3−i3i3i3−i3−i3i3i30000220011i3i3−i3−i3i3i3−i3−i3-1-1-1-1−i3i3−i3i3000000000000
χ28222222-12-2222-2-1-1-1-1-1-1-1-2-2-2-1-1-2-2-2-20000-1-1111111111111i3i3−i3−i3i3i3−i3−i30000220011−i3−i3i3i3−i3−i3i3i3-1-1-1-1i3−i3i3−i3000000000000
χ29222222-1-22-2-2-22-1-1-111112-2-2-1-12i2i−2i−2i00001111-1-1−i−i−i−iiiii33−3−3−3−3330000−2i2i001-1−i3−i3i3i3i3i3−i3−i3ii−i−i3−3−33000000000000
χ30222222-1-22-2-2-22-1-1-111112-2-2-1-12i2i−2i−2i00001111-1-1−i−i−i−iiiii−3−33333−3−30000−2i2i001-1i3i3−i3−i3−i3−i3i3i3ii−i−i−333−3000000000000
χ31222222-1-22-2-2-22-1-1-111112-2-2-1-1−2i−2i2i2i00001111-1-1iiii−i−i−i−i33−3−3−3−33300002i−2i001-1i3i3−i3−i3−i3−i3i3i3−i−iii3−3−33000000000000
χ32222222-1-22-2-2-22-1-1-111112-2-2-1-1−2i−2i2i2i00001111-1-1iiii−i−i−i−i−3−33333−3−300002i−2i001-1−i3−i3i3i3i3i3−i3−i3−i−iii−333−3000000000000
χ33222222-1-2-2-2-2-2-2-1-1-11111-222-1-12i2i−2i−2i2i2i−2i−2i11-1-111−i−i−i−iiiii−i−i−i−iiiii2-22-22i−2i2i−2i-11-1-1-1-11111−i−iii−i−iii000000000000
χ34222222-1-2-2-2-2-2-2-1-1-11111-222-1-12i2i−2i−2i−2i−2i2i2i11-1-111−i−i−i−iiiiiiiii−i−i−i−i-22-222i−2i−2i2i-111111-1-1-1-1−i−iiiii−i−i000000000000
χ35222222-1-2-2-2-2-2-2-1-1-11111-222-1-1−2i−2i2i2i2i2i−2i−2i11-1-111iiii−i−i−i−i−i−i−i−iiiii-22-22−2i2i2i−2i-111111-1-1-1-1ii−i−i−i−iii000000000000
χ36222222-1-2-2-2-2-2-2-1-1-11111-222-1-1−2i−2i2i2i−2i−2i2i2i11-1-111iiii−i−i−i−iiiii−i−i−i−i2-22-2−2i2i−2i2i-11-1-1-1-11111ii−i−iii−i−i000000000000
χ372222-2-2222-2-222222-2-2-2-2-2-22-2-20000000022-2-222000000000000000022-2-200002-22-22-22-22-200000000000000000000
χ382222-2-2222-2-222222-2-2-2-2-2-22-2-20000000022-2-2220000000000000000-2-22200002-2-22-22-22-2200000000000000000000
χ392222-2-222-2-2-22-2222-2-2-2-222-2-2-200002i2i−2i−2i2222-2-2000000002i2i2i2i−2i−2i−2i−2i000000−2i2i-22000000000000−2i−2i2i2i000000000000
χ402222-2-222-2-2-22-2222-2-2-2-222-2-2-20000−2i−2i2i2i2222-2-200000000−2i−2i−2i−2i2i2i2i2i0000002i−2i-220000000000002i2i−2i−2i000000000000
χ412222-2-22-2222-222222222-22-2-2-200002222-2-222220000000022222222000000-2-2-2-2000000000000-2-2-2-2000000000000
χ422222-2-22-2222-222222222-22-2-2-20000-2-2-2-2-2-2222200000000-2-2-2-2-2-2-2-200000022-2-20000000000002222000000000000
χ432222-2-22-2-222-2-222222222-22-2-200000000-2-2-2-2-2-200000000000000002-2-220000222-22-2-22-2200000000000000000000
χ442222-2-22-2-222-2-222222222-22-2-200000000-2-2-2-2-2-20000000000000000-222-2000022-22-222-22-200000000000000000000
χ452222-2-2-122-2-222-1-1-11111-2-221100000000-1-111-1-133−3−333−3−333−3−3−3−33322-2-20000-11-11-11-11-113−33−3−333−3000000000000
χ462222-2-2-122-2-222-1-1-11111-2-221100000000-1-111-1-133−3−333−3−3−3−33333−3−3-2-2220000-111-11-11-11-13−33−33−3−33000000000000
χ472222-2-2-122-2-222-1-1-11111-2-221100000000-1-111-1-1−3−333−3−33333−3−3−3−333-2-2220000-111-11-11-11-1−33−33−333−3000000000000
χ482222-2-2-122-2-222-1-1-11111-2-221100000000-1-111-1-1−3−333−3−333−3−33333−3−322-2-20000-11-11-11-11-11−33−333−3−33000000000000
χ492222-2-2-12-2-2-22-2-1-1-1111122-21100002i2i−2i−2i-1-1-1-11133−3−333−3−3−i−i−i−iiiii000000−2i2i1-1−i3i3i3−i3−i3i3i3−i3−33−33ii−i−i000000000000
χ502222-2-2-12-2-2-22-2-1-1-1111122-21100002i2i−2i−2i-1-1-1-111−3−333−3−333−i−i−i−iiiii000000−2i2i1-1i3−i3−i3i3i3−i3−i3i33−33−3ii−i−i000000000000
χ512222-2-2-12-2-2-22-2-1-1-1111122-2110000−2i−2i2i2i-1-1-1-11133−3−333−3−3iiii−i−i−i−i0000002i−2i1-1i3−i3−i3i3i3−i3−i3i3−33−33−i−iii000000000000
χ522222-2-2-12-2-2-22-2-1-1-1111122-2110000−2i−2i2i2i-1-1-1-111−3−333−3−333iiii−i−i−i−i0000002i−2i1-1−i3i3i3−i3−i3i3i3−i33−33−3−i−iii000000000000
χ532222-2-2-1-2222-22-1-1-1-1-1-1-1-22-2110000222211-1-1-1-1−i3−i3i3i3i3i3−i3−i3-1-1-1-1-1-1-1-1000000-2-211−i3i3i3−i3i3−i3−i3i3i3−i3−i3i31111000000000000
χ542222-2-2-1-2222-22-1-1-1-1-1-1-1-22-2110000222211-1-1-1-1i3i3−i3−i3−i3−i3i3i3-1-1-1-1-1-1-1-1000000-2-211i3−i3−i3i3−i3i3i3−i3−i3i3i3−i31111000000000000
χ552222-2-2-1-2222-22-1-1-1-1-1-1-1-22-2110000-2-2-2-211-1-1-1-1−i3−i3i3i3i3i3−i3−i3111111110000002211i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3-1-1-1-1000000000000
χ562222-2-2-1-2222-22-1-1-1-1-1-1-1-22-2110000-2-2-2-211-1-1-1-1i3i3−i3−i3−i3−i3i3i3111111110000002211−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3-1-1-1-1000000000000
χ572222-2-2-1-2-222-2-2-1-1-1-1-1-1-12-221100000000111111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i32-2-220000-1-1-11-111-11-1−i3i3i3−i3i3−i3i3−i3000000000000
χ582222-2-2-1-2-222-2-2-1-1-1-1-1-1-12-221100000000111111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-222-20000-1-11-11-1-11-11−i3i3i3−i3−i3i3−i3i3000000000000
χ592222-2-2-1-2-222-2-2-1-1-1-1-1-1-12-221100000000111111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-222-20000-1-11-11-1-11-11i3−i3−i3i3i3−i3i3−i3000000000000
χ602222-2-2-1-2-222-2-2-1-1-1-1-1-1-12-221100000000111111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i32-2-220000-1-1-11-111-11-1i3−i3−i3i3−i3i3−i3i3000000000000
χ6122-2-22-22202-2-202-2-222-2-20002-22-22-200002-200002-22-22-22-200000000000000000000000000000000002−22−22−22−20000
χ6222-2-22-22202-2-202-2-222-2-20002-22-22-200002-200002-22-22-22-20000000000000000000000000000000000−22−22−22−220000
χ6322-2-22-22202-2-202-2-222-2-20002-2-22-2200002-20000-22-22-22-2200000000000000000000000000000000002−22−2−22−220000
χ6422-2-22-22202-2-202-2-222-2-20002-2-22-2200002-20000-22-22-22-220000000000000000000000000000000000−22−222−22−20000
χ6522-2-22-22-20-22202-2-2-2-2220002-22i−2i−2i2i0000-2200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000−i2i2i2−i2−222−20000
χ6622-2-22-22-20-22202-2-2-2-2220002-22i−2i−2i2i0000-2200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000i2−i2−i2i22−2−220000
χ6722-2-22-22-20-22202-2-2-2-2220002-2−2i2i2i−2i0000-220000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000−i2i2i2−i22−2−220000
χ6822-2-22-22-20-22202-2-2-2-2220002-2−2i2i2i−2i0000-220000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000i2−i2−i2i2−222−20000
χ6944-4-44-4-2404-4-40-222-2-222000-224-44-40000-220000-22-22-22-220000000000000000000000000000000000000000000000
χ7044-4-44-4-2404-4-40-222-2-222000-22-44-440000-2200002-22-22-22-20000000000000000000000000000000000000000000000
χ7144-4-44-4-2-40-4440-22222-2-2000-224i−4i−4i4i00002-20000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ7244-4-44-4-2-40-4440-22222-2-2000-22−4i4i4i−4i00002-200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ7344-4-4-44440-44-404-4-4-4-444000-44000000004-40000000000000000000000000000000000000000000000000000000000
χ7444-4-4-444-404-4404-4-444-4-4000-4400000000-440000000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-240-44-40-22222-2-20002-200000000-22000023−23−232323−23−23230000000000000000000000000000000000000000000000
χ7644-4-4-44-240-44-40-22222-2-20002-200000000-220000−232323−23−232323−230000000000000000000000000000000000000000000000
χ7744-4-4-44-2-404-440-222-2-2220002-2000000002-20000−2i32i32i3−2i32i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ7844-4-4-44-2-404-440-222-2-2220002-2000000002-200002i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ794-44-400404000-4-44-4000000000000022−2222−2200004-40000000022−2222−2222−2222−2200000000000000000000000000000000000000
χ804-44-400404000-4-44-40000000000000−2222−222200004-400000000−2222−2222−2222−222200000000000000000000000000000000000000
χ814-44-40040-40004-44-40000000000000−2i22i22i2−2i20000-4400000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ824-44-40040-40004-44-400000000000002i2−2i2−2i22i20000-44000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ834-44-400-204000-42-2223−2323−2300000000022−2222−220023−23-22000000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2300000000000000000000000000000000000000
χ844-44-400-204000-42-2223−2323−23000000000−2222−22220023−23-2200000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2300000000000000000000000000000000000000
χ854-44-400-204000-42-22−2323−232300000000022−2222−2200−2323-22000000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000000000
χ864-44-400-204000-42-22−2323−2323000000000−2222−222200−2323-2200000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000000000
χ874-44-400-20-400042-2223−2323−23000000000−2i22i22i2−2i200−23232-2000000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000000000000000
χ884-44-400-20-400042-2223−2323−230000000002i2−2i2−2i22i200−23232-200000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000000000000000
χ894-44-400-20-400042-22−2323−2323000000000−2i22i22i2−2i20023−232-2000000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000000000
χ904-44-400-20-400042-22−2323−23230000000002i2−2i2−2i22i20023−232-200000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ232ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000000000
χ918-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-8800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000000000
χ938-8-8800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000000000

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