Finite Group Databasebeta

← Group #10705582

Character table — Group #10705582

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order12222234444666121212122244444466666612121212121224668888888812121212121224242424242424242424242424242424888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111iiii−i−i−i−i-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111iiii−i−i−i−i-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ7111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111−i−i−i−iiiii-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111−i−i−i−iiiii-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ91111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-1-1ii−i−iii−i−i11-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-1-1ii−i−iii−i−i11-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-1-1−i−iii−i−iii11-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-1-1−i−iii−i−iii11-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ141111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ151111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ161111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222222222-2-222-2-2222222222222-2-2-2-200000000-2-2-2-2-2-20000000000000000000000000000
χ18222222222222222222-2-222-2-22222-2-2-2-222-2-2-2-2-2-2-2-2000000002222-2-20000000000000000000000000000
χ192222222-2-2-2-2222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-22-22200000000-2-222-2-20000000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-2-2-22222-2-222-2-2-2-2-2-222222-2220000000022-2-2-2-20000000000000000000000000000
χ21222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111000000000000
χ23222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-21100000000111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ24222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-21100000000111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-222-2-222-1-11111-1-11111-2-21100000000-1-1-1-11133−3−333−3−3−3−333−3−333000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-222-2-222-1-11111-1-11111-2-21100000000-1-1-1-111−3−333−3−33333−3−333−3−3000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1111122-1-12i2i2i2i−2i−2i−2i−2i1111-1-1−i−i−i−i−i−i−i−iiiiiiiii000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1111122-1-1−2i−2i−2i−2i2i2i2i2i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i000000000000
χ29222222-1-2-2-2-2-1-1-111112222-2-2-2-2-1-1-1-1-1-1111111-22112i2i−2i−2i2i2i−2i−2i-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii000000000000
χ30222222-1-2-2-2-2-1-1-111112222-2-2-2-2-1-1-1-1-1-1111111-2211−2i−2i2i2i−2i−2i2i2i-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i000000000000
χ31222222-1-2-2-2-2-1-1-1111122-2-2-2-222-1-1-1-1-1-11111112-2-1-10000000011-1-11133−3−3−3−33333−3−3−3−333000000000000
χ32222222-1-2-2-2-2-1-1-1111122-2-2-2-222-1-1-1-1-1-11111112-2-1-10000000011-1-111−3−33333−3−3−3−33333−3−3000000000000
χ33222222-1-2-2-2-2-1-1-11111-2-22222-2-2-1-1111111-1-1-1-12-2-1-100000000-1-11111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000
χ34222222-1-2-2-2-2-1-1-11111-2-22222-2-2-1-1111111-1-1-1-12-2-1-100000000-1-11111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000
χ35222222-1-2-2-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-1-221122-2-2-2-22211-1-1-1-1-1-1-1-111111111-1-1-1-1000000000000
χ36222222-1-2-2-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-1-2211-2-22222-2-211-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000
χ372-22-22-222i2i−2i−2i2-2-22i2i−2i−2i002i−2i002-22-200002i−2i000000002−2−i2i2−i2i22−22i−2i2-2002−22−2−i2i2−i2i2−i2i2−i2i22−22−2000000000000
χ382-22-22-222i2i−2i−2i2-2-22i2i−2i−2i002i−2i002-22-200002i−2i00000000−22i2−i2i2−i2−222i−2i2-200−22−22i2−i2i2−i2i2−i2i2−i2−22−22000000000000
χ392-22-22-222i2i−2i−2i2-2-22i2i−2i−2i00−2i2i00-222-200002i−2i00000000−i2i2−222−2i2−i2−2i2i-2200−i2i2−i2i2−22−222−22−2i2−i2i2−i2000000000000
χ402-22-22-222i2i−2i−2i2-2-22i2i−2i−2i00−2i2i00-222-200002i−2i00000000i2−i22−2−22−i2i2−2i2i-2200i2−i2i2−i22−22−2−22−22−i2i2−i2i2000000000000
χ412-22-22-22−2i−2i2i2i2-2-2−2i−2i2i2i002i−2i00-222-20000−2i2i00000000−i2i22−2−22i2−i22i−2i-2200−i2i2−i2i22−22−2−22−22i2−i2i2−i2000000000000
χ422-22-22-22−2i−2i2i2i2-2-2−2i−2i2i2i002i−2i00-222-20000−2i2i00000000i2−i2−222−2−i2i22i−2i-2200i2−i2i2−i2−22−222−22−2−i2i2−i2i2000000000000
χ432-22-22-22−2i−2i2i2i2-2-2−2i−2i2i2i00−2i2i002-22-20000−2i2i000000002−2i2−i2i2−i22−2−2i2i2-2002−22−2i2−i2i2−i2i2−i2i2−i22−22−2000000000000
χ442-22-22-22−2i−2i2i2i2-2-2−2i−2i2i2i00−2i2i002-22-20000−2i2i00000000−22−i2i2−i2i2−22−2i2i2-200−22−22−i2i2−i2i2−i2i2−i2i2−22−22000000000000
χ452-22-22-2-12i2i−2i−2i-111−i−iii002i−2i002-2-11−i3−i3i3i3−ii33−3−300−i3i32−2−i2i2−i2i22−2−ii-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ462-22-22-2-12i2i−2i−2i-111−i−iii002i−2i002-2-11−i3−i3i3i3−ii33−3−300−i3i3−22i2−i2i2−i2−22−ii-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ472-22-22-2-12i2i−2i−2i-111−i−iii002i−2i002-2-11i3i3−i3−i3−ii−3−33300i3−i32−2−i2i2−i2i22−2−ii-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ482-22-22-2-12i2i−2i−2i-111−i−iii002i−2i002-2-11i3i3−i3−i3−ii−3−33300i3−i3−22i2−i2i2−i2−22−ii-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ492-22-22-2-12i2i−2i−2i-111−i−iii00−2i2i00-22-11−i3−i3i3i3−ii33−3−300i3−i3−i2i2−222−2i2−i2i−i1-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ502-22-22-2-12i2i−2i−2i-111−i−iii00−2i2i00-22-11−i3−i3i3i3−ii33−3−300i3−i3i2−i22−2−22−i2i2i−i1-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ512-22-22-2-12i2i−2i−2i-111−i−iii00−2i2i00-22-11i3i3−i3−i3−ii−3−33300−i3i3−i2i2−222−2i2−i2i−i1-13−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ522-22-22-2-12i2i−2i−2i-111−i−iii00−2i2i00-22-11i3i3−i3−i3−ii−3−33300−i3i3i2−i22−2−22−i2i2i−i1-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ532-22-22-2-1−2i−2i2i2i-111ii−i−i002i−2i00-22-11−i3−i3i3i3i−i−3−33300i3−i3−i2i22−2−22i2−i2−ii1-13−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ542-22-22-2-1−2i−2i2i2i-111ii−i−i002i−2i00-22-11−i3−i3i3i3i−i−3−33300i3−i3i2−i2−222−2−i2i2−ii1-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ552-22-22-2-1−2i−2i2i2i-111ii−i−i002i−2i00-22-11i3i3−i3−i3i−i33−3−300−i3i3−i2i22−2−22i2−i2−ii1-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ562-22-22-2-1−2i−2i2i2i-111ii−i−i002i−2i00-22-11i3i3−i3−i3i−i33−3−300−i3i3i2−i2−222−2−i2i2−ii1-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ572-22-22-2-1−2i−2i2i2i-111ii−i−i00−2i2i002-2-11−i3−i3i3i3i−i−3−33300−i3i32−2i2−i2i2−i22−2i−i-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ582-22-22-2-1−2i−2i2i2i-111ii−i−i00−2i2i002-2-11−i3−i3i3i3i−i−3−33300−i3i3−22−i2i2−i2i2−22i−i-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ592-22-22-2-1−2i−2i2i2i-111ii−i−i00−2i2i002-2-11i3i3−i3−i3i−i33−3−300i3−i32−2i2−i2i2−i22−2i−i-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ602-22-22-2-1−2i−2i2i2i-111ii−i−i00−2i2i002-2-11i3i3−i3−i3i−i33−3−300i3−i3−22−i2i2−i2i2−22i−i-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ612-22-2-2222i−2i2i−2i2-2-22i2i−2i−2i2-2002i−2i00-222-22-2−2i2i2i−2i2i−2i00000000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ622-22-2-2222i−2i2i−2i2-2-22i2i−2i−2i2-2002i−2i00-222-22-2−2i2i2i−2i2i−2i0000000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ632-22-2-2222i−2i2i−2i2-2-22i2i−2i−2i-2200−2i2i00-22-22-22−2i2i−2i2i−2i2i00000000000000000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i0000
χ642-22-2-2222i−2i2i−2i2-2-22i2i−2i−2i-2200−2i2i00-22-22-22−2i2i−2i2i−2i2i0000000000000000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i0000
χ652-22-2-222−2i2i−2i2i2-2-2−2i−2i2i2i2-200−2i2i00-222-22-22i−2i−2i2i−2i2i00000000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ662-22-2-222−2i2i−2i2i2-2-2−2i−2i2i2i2-200−2i2i00-222-22-22i−2i−2i2i−2i2i0000000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ672-22-2-222−2i2i−2i2i2-2-2−2i−2i2i2i-22002i−2i00-22-22-222i−2i2i−2i2i−2i00000000000000000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i0000
χ682-22-2-222−2i2i−2i2i2-2-2−2i−2i2i2i-22002i−2i00-22-22-222i−2i2i−2i2i−2i0000000000000000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i0000
χ694444-4-444-4-44444444400000000-4-40000-4-400000000000000000000000000000000000000000000000000
χ704444-4-44-444-4444-4-4-4-400000000-4-400004400000000000000000000000000000000000000000000000000
χ714444-4-4-24-4-44-2-2-2-2-2-2-20000000022−2i32i32i3−2i322−2i32i32i3−2i30000000000000000000000000000000000000000000000
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χ784-44-4-44-2−4i4i−4i4i-2222i2i−2i−2i-44004i−4i002-22-22-2−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ7988-8-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-400004-4443−4343−43000000000000000000000000000000000000000000000000000000000000000000
χ8188-8-800-400004-44−4343−4343000000000000000000000000000000000000000000000000000000000000000000
χ828-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800-4000044-4−4i34i34i3−4i3000000000000000000000000000000000000000000000000000000000000000000
χ848-8-8800-4000044-44i3−4i3−4i34i3000000000000000000000000000000000000000000000000000000000000000000

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