Finite Group Databasebeta

← Group #10693847

Character table — Group #10693847

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222222222222222222224444444444444444444444444444448888888888888888888888881212121212121212121212121212121248484848
order122222223444444446666666888888881212121212121212448888121212121212121224242424242424242424242424242424888888882424242424242424242424242424242444444444888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ91-1111-1-1-111-1-1-1111-1-1-1-1-11111111-1-1-1-111-1-1-1-1111-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−ii−ii−i
χ101-1111-1-1-111-1-1-1111-1-1-1-1-11111111-1-1-1-111-1-1-1-1111-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−ii−ii
χ111-1111-1-1-111-1-1-1111-1-1-1-1-11111111-1-1-1-111-1-1-1-1111-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−i−ii−ii
χ121-1111-1-1-111-1-1-1111-1-1-1-1-11111111-1-1-1-111-1-1-1-1111-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−i−iii−i−iii−i−i−i−iiiiii−ii−i
χ131-1111-1-1-111-1-1-1111-1-1-1-1-1111-1-1-1-1111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiiii−i−ii
χ141-1111-1-1-111-1-1-1111-1-1-1-1-1111-1-1-1-1111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i−iii−i
χ151-1111-1-1-111-1-1-1111-1-1-1-1-1111-1-1-1-1111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−i−i−i−i−iiiii−iii−i
χ161-1111-1-1-111-1-1-1111-1-1-1-1-1111-1-1-1-1111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iiiiiii−i−i−i−ii−i−ii
χ17222222222222-2-2-22-222222220000000022222222-2-20000-2-2-2-2-2-2-2-200000000000000000000000000000000000000002222-2-2-2-2000000000000
χ18222222222222-2-2-22-222222220000000022222222-2-20000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-2-2-22222000000000000
χ19222222222-2-2-2222-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ20222222222-2-2-2222-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-2222222200000000-2-2-2-2-2-2-2-222000022-2-222-2-20000000000000000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i0000
χ22222222222-2-2-2-2-2-2-2-2222222200000000-2-2-2-2-2-2-2-222000022-2-222-2-2000000000000000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000
χ2322222222-122222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ2522222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000
χ2622222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000
χ2722222222-1-2-2-2222-22-1-1-1-1-1-1-12222222211111111-2-2-2-2-2-211-1-111-1-1-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−300000000000000000000
χ2822222222-1-2-2-2222-22-1-1-1-1-1-1-12222222211111111-2-2-2-2-2-211-1-111-1-1-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−33300000000000000000000
χ2922222222-1-2-2-2222-22-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-2-2222211-1-111-1-11111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−33300000000000000000000
χ3022222222-1-2-2-2222-22-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-2-2222211-1-111-1-11111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−300000000000000000000
χ31222-2-22-2-2222-2000-2022-2-22-2-222−2−222−2−22222-2-2-2-2002−22−20000000022−2−222−2−222−2−222−2−20000000000000000000000002-22-200002−22−22−22−20000
χ32222-2-22-2-2222-2000-2022-2-22-2-222−2−222−2−22222-2-2-2-2002−22−20000000022−2−222−2−222−2−222−2−2000000000000000000000000-22-220000−22−22−22−220000
χ33222-2-22-2-2222-2000-2022-2-22-2-2−2−222−2−2222222-2-2-2-200−22−2200000000−2−222−2−222−2−222−2−2220000000000000000000000002-22-20000−22−22−22−220000
χ34222-2-22-2-2222-2000-2022-2-22-2-2−2−222−2−2222222-2-2-2-200−22−2200000000−2−222−2−222−2−222−2−222000000000000000000000000-22-2200002−22−22−22−20000
χ35222-2-22-2-22-2-220002022-2-22-2-222−2−222−2−2-2-2-2-2222200−22−220000000022−2−2−2−22222−2−2−2−22200000000000000000000000000002i−2i2i−2i−i2i2i2−i2−i2i2i2−i20000
χ36222-2-22-2-22-2-220002022-2-22-2-222−2−222−2−2-2-2-2-2222200−22−220000000022−2−2−2−22222−2−2−2−2220000000000000000000000000000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i20000
χ37222-2-22-2-22-2-220002022-2-22-2-2−2−222−2−222-2-2-2-22222002−22−200000000−2−22222−2−2−2−22222−2−200000000000000000000000000002i−2i2i−2ii2−i2−i2i2i2−i2−i2i20000
χ38222-2-22-2-22-2-220002022-2-22-2-2−2−222−2−222-2-2-2-22222002−22−200000000−2−22222−2−2−2−22222−2−20000000000000000000000000000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i20000
χ3922-22-2-22-22000-22-2022-22-2-22-22i−2i2i−2i2i−2i2i−2i00000000000000002-2002-22i−2i2i−2i00002i−2i2i−2i0000−i2i2−i2i22−22−2−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000000000000000
χ4022-22-2-22-22000-22-2022-22-2-22-22i−2i2i−2i2i−2i2i−2i00000000000000002-2002-22i−2i2i−2i00002i−2i2i−2i0000i2−i2i2−i2−22−22i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000000000000000
χ4122-22-2-22-22000-22-2022-22-2-22-2−2i2i−2i2i−2i2i−2i2i00000000000000002-2002-2−2i2i−2i2i0000−2i2i−2i2i0000−i2i2−i2i2−22−22−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000000000000000
χ4222-22-2-22-22000-22-2022-22-2-22-2−2i2i−2i2i−2i2i−2i2i00000000000000002-2002-2−2i2i−2i2i0000−2i2i−2i2i0000i2−i2i2−i22−22−2i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000000000000000
χ4322-22-2-22-2-1000-22-202-11-111-112i−2i2i−2i2i−2i2i−2i3−33−33−33−30000003−3-113−3-11−ii−ii−i3i3−i3i3−ii−ii−i3i3−i3i3−i2i2−i2i22−22−2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000000000
χ4422-22-2-22-2-1000-22-202-11-111-112i−2i2i−2i2i−2i2i−2i3−33−33−33−30000003−3-113−3-11−ii−ii−i3i3−i3i3−ii−ii−i3i3−i3i3i2−i2i2−i2−22−22−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000000000
χ4522-22-2-22-2-1000-22-202-11-111-112i−2i2i−2i2i−2i2i−2i−33−33−33−33000000−33-11−33-11−ii−iii3−i3i3−i3−ii−iii3−i3i3−i3−i2i2−i2i22−22−2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000000000
χ4622-22-2-22-2-1000-22-202-11-111-112i−2i2i−2i2i−2i2i−2i−33−33−33−33000000−33-11−33-11−ii−iii3−i3i3−i3−ii−iii3−i3i3−i3i2−i2i2−i2−22−22−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000000000
χ4722-22-2-22-2-1000-22-202-11-111-11−2i2i−2i2i−2i2i−2i2i3−33−33−33−30000003−3-113−3-11i−ii−ii3−i3i3−i3i−ii−ii3−i3i3−i3−i2i2−i2i2−22−22ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000000000
χ4822-22-2-22-2-1000-22-202-11-111-11−2i2i−2i2i−2i2i−2i2i3−33−33−33−30000003−3-113−3-11i−ii−ii3−i3i3−i3i−ii−ii3−i3i3−i3i2−i2i2−i22−22−2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000000000
χ4922-22-2-22-2-1000-22-202-11-111-11−2i2i−2i2i−2i2i−2i2i−33−33−33−33000000−33-11−33-11i−ii−i−i3i3−i3i3i−ii−i−i3i3−i3i3−i2i2−i2i2−22−22ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000000000
χ5022-22-2-22-2-1000-22-202-11-111-11−2i2i−2i2i−2i2i−2i2i−33−33−33−33000000−33-11−33-11i−ii−i−i3i3−i3i3i−ii−i−i3i3−i3i3i2−i2i2−i22−22−2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000000000
χ512-2222-2-2-222-2-22-2-222-2-2-2-22220000000022-2-2-2-222-220000-2-22222-2-200000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ522-2222-2-2-222-2-22-2-222-2-2-2-22220000000022-2-2-2-222-220000-2-22222-2-20000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ532-2222-2-2-22-2222-2-2-22-2-2-2-222200000000-2-22222-2-22-200002222-2-2-2-200000000000000000000000000000000000000000000000022-2-2-2-2220000
χ542-2222-2-2-22-2222-2-2-22-2-2-2-222200000000-2-22222-2-22-200002222-2-2-2-2000000000000000000000000000000000000000000000000-2-22222-2-20000
χ552-2222-2-2-22-222-222-2-2-2-2-2-22222222-2-2-2-2-2-22222-2-2-22-2-222-2-2-2-222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ562-2222-2-2-22-222-222-2-2-2-2-2-2222-2-2-2-22222-2-22222-2-2-2222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-200000000000000000000000000000000000000000000
χ572-2222-2-2-2-12-2-2-2222-21111-1-1-12222-2-2-2-2-1-11111-1-12-222-2-2-1-11111-1-1-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-1111100000000000000000000
χ582-2222-2-2-2-12-2-2-2222-21111-1-1-12222-2-2-2-2-1-11111-1-12-222-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-100000000000000000000
χ592-2222-2-2-2-12-2-2-2222-21111-1-1-1-2-2-2-22222-1-11111-1-12-2-2-222-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-100000000000000000000
χ602-2222-2-2-2-12-2-2-2222-21111-1-1-1-2-2-2-22222-1-11111-1-12-2-2-222-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-1111100000000000000000000
χ612-2222-2-2-2-1-222-222-2-21111-1-1-12222-2-2-2-211-1-1-1-111-22-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000033−3−3−3−33333−3−3−3−33300000000000000000000
χ622-2222-2-2-2-1-222-222-2-21111-1-1-12222-2-2-2-211-1-1-1-111-22-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−3−33333−3−3−3−33333−3−300000000000000000000
χ632-2222-2-2-2-1-222-222-2-21111-1-1-1-2-2-2-2222211-1-1-1-111-2222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−300000000000000000000
χ642-2222-2-2-2-1-222-222-2-21111-1-1-1-2-2-2-2222211-1-1-1-111-2222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−33300000000000000000000
χ652-22-2-2-22222-22000-20-2-2222-2-222−2−2−2−22222-2-222-2-2002−2−220000000022−2−222−2−2−2−222−2−2220000000000000000000000002i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i20000
χ662-22-2-2-22222-22000-20-2-2222-2-222−2−2−2−22222-2-222-2-2002−2−220000000022−2−222−2−2−2−222−2−222000000000000000000000000−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i20000
χ672-22-2-2-22222-22000-20-2-2222-2-2−2−22222−2−222-2-222-2-200−222−200000000−2−222−2−22222−2−222−2−20000000000000000000000002i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i20000
χ682-22-2-2-22222-22000-20-2-2222-2-2−2−22222−2−222-2-222-2-200−222−200000000−2−222−2−22222−2−222−2−2000000000000000000000000−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i20000
χ692-22-2-2-2222-22-200020-2-2222-2-222−2−2−2−222-2-222-2-22200−222−20000000022−2−2−2−222−2−22222−2−200000000000000000000000000002-2-22−222−22−2−220000
χ702-22-2-2-2222-22-200020-2-2222-2-222−2−2−2−222-2-222-2-22200−222−20000000022−2−2−2−222−2−22222−2−20000000000000000000000000000-222-22−2−22−222−20000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.