Finite Group Databasebeta

← Group #10690002

Character table — Group #10690002

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order12222222344444444666666612121212121212122222448888888812121212121212122424242424242424242424242424242444666688881212121224242424242424244444444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111111111-1-1
χ91-1-111-11-1111-11-1-1-11-1-1-1-11111111-1-1-1-111-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-111-1-1ii−i−i11-1-1iiii−i−i−i−iii−i−ii−iii−i−i11-1-11-1
χ101-1-111-11-1111-11-1-1-11-1-1-1-11111111-1-1-1-111-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-111-1-1ii−i−i11-1-1iiii−i−i−i−i−i−iii−ii−i−iii-1-111-11
χ111-1-111-11-1111-11-1-1-11-1-1-1-11111111-1-1-1-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-111-1-1−i−iii11-1-1−i−i−i−iiiiiii−i−ii−iii−i−i-1-111-11
χ121-1-111-11-1111-11-1-1-11-1-1-1-11111111-1-1-1-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-111-1-1−i−iii11-1-1−i−i−i−iiiii−i−iii−ii−i−iii11-1-11-1
χ131-1-111-11-1111-11-1-1-11-1-1-1-11111111-1-1-1-1-1-1111-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-1-111−i−iii-1-111−i−i−i−iiiiiii−i−ii−i−i−iii11-1-1-11
χ141-1-111-11-1111-11-1-1-11-1-1-1-11111111-1-1-1-1-1-1111-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-1-111−i−iii-1-111−i−i−i−iiiii−i−iii−iiii−i−i-1-1111-1
χ151-1-111-11-1111-11-1-1-11-1-1-1-11111111-1-1-1-1-1-1111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-1-111ii−i−i-1-111iiii−i−i−i−iii−i−ii−i−i−iii-1-1111-1
χ161-1-111-11-1111-11-1-1-11-1-1-1-11111111-1-1-1-1-1-1111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-1-111ii−i−i-1-111iiii−i−i−i−i−i−iii−iiii−i−i11-1-1-11
χ17222222222222-2-2-22-22222222222222220000-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000002222-2-20000000000
χ18222222222222-2-2-22-22222222222222220000-2-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000-2-2-2-2220000000000
χ19222222222-2-2-2222-222222222-2-2-2-2-2-2-2-22222-2-20000000022-2-222-2-20000000000000000-2-222220000-2-2-2-2000000000000000000000000
χ20222222222-2-2-2222-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-222-2-2000000000000000022-2-2-2-200002222000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200002200000000-2-222-2-222000000000000000000000000000000000000000000002-22-2000000
χ22222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200002200000000-2-222-2-22200000000000000000000000000000000000000000000-22-22000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-1-1-1-1-2-2-2-2-1-1-1-1111111110000000000000000
χ2522222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2-2-21111111111110000000000000000
χ2622222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2111122221111-1-1-1-1-1-1-1-10000000000000000
χ2722222222-1-2-2-2222-22-1-1-1-1-1-1-1111111112222-2-200000000-1-111-1-1113333−3−3−3−33333−3−3−3−3-2-2-1-1-1-10000111133−3−333−3−30000000000000000
χ2822222222-1-2-2-2222-22-1-1-1-1-1-1-1111111112222-2-200000000-1-111-1-111−3−3−3−33333−3−3−3−33333-2-2-1-1-1-100001111−3−333−3−3330000000000000000
χ2922222222-1-2-2-2222-22-1-1-1-1-1-1-111111111-2-2-2-2-2-200000000-1-111-1-1113333−3−3−3−33333−3−3−3−32211110000-1-1-1-1−3−333−3−3330000000000000000
χ3022222222-1-2-2-2222-22-1-1-1-1-1-1-111111111-2-2-2-2-2-200000000-1-111-1-111−3−3−3−33333−3−3−3−333332211110000-1-1-1-133−3−333−3−30000000000000000
χ31222-2-2-22-22000-22-20222-2-22-2-2000000002-22-200−i2−i2i2i2−i2−i2i2i22-2002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002-22-2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i20000000000000000
χ32222-2-2-22-22000-22-20222-2-22-2-2000000002-22-200i2i2−i2−i2i2i2−i2−i22-2002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002-22-2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i20000000000000000
χ33222-2-2-22-22000-22-20222-2-22-2-200000000-22-2200−i2−i2i2i2−i2−i2i2i22-2002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200-22-22i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i20000000000000000
χ34222-2-2-22-22000-22-20222-2-22-2-200000000-22-2200i2i2−i2−i2i2i2−i2−i22-2002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200-22-22−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i20000000000000000
χ35222-2-2-22-2-1000-22-202-1-111-11133−3−33−33−32-22-200−i2−i2i2i2−i2−i2i2i2-113−3-113−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300-11-11−i2i2−i2i23−33−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ36222-2-2-22-2-1000-22-202-1-111-11133−3−33−33−32-22-200i2i2−i2−i2i2i2−i2−i2-113−3-113−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300-11-11i2−i2i2−i23−33−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ37222-2-2-22-2-1000-22-202-1-111-11133−3−33−33−3-22-2200−i2−i2i2i2−i2−i2i2i2-113−3-113−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23001-11-1i2−i2i2−i2−33−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ38222-2-2-22-2-1000-22-202-1-111-11133−3−33−33−3-22-2200i2i2−i2−i2i2i2−i2−i2-113−3-113−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23001-11-1−i2i2−i2i2−33−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ39222-2-2-22-2-1000-22-202-1-111-111−3−333−33−332-22-200−i2−i2i2i2−i2−i2i2i2-11−33-11−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700-11-11−i2i2−i2i2−33−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ40222-2-2-22-2-1000-22-202-1-111-111−3−333−33−332-22-200i2i2−i2−i2i2i2−i2−i2-11−33-11−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700-11-11i2−i2i2−i2−33−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ41222-2-2-22-2-1000-22-202-1-111-111−3−333−33−33-22-2200−i2−i2i2i2−i2−i2i2i2-11−33-11−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7001-11-1i2−i2i2−i23−33−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ42222-2-2-22-2-1000-22-202-1-111-111−3−333−33−33-22-2200i2i2−i2−i2i2i2−i2−i2-11−33-11−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7001-11-1−i2i2−i2i23−33−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ4322-2-222-2-222-2-2000202-22-2-2-222-22-2-2-2220000002−22−22−22−2000000002−22−22−22−22−22−22−22−200000000000000000000002i−2i2i−2i000000−i2i2−i2i200
χ4422-2-222-2-222-2-2000202-22-2-2-222-22-2-2-2220000002−22−22−22−2000000002−22−22−22−22−22−22−22−20000000000000000000000−2i2i−2i2i000000i2−i2i2−i200
χ4522-2-222-2-222-2-2000202-22-2-2-222-22-2-2-222000000−22−22−22−2200000000−22−22−22−22−22−22−22−2200000000000000000000002i−2i2i−2i000000i2−i2i2−i200
χ4622-2-222-2-222-2-2000202-22-2-2-222-22-2-2-222000000−22−22−22−2200000000−22−22−22−22−22−22−22−220000000000000000000000−2i2i−2i2i000000−i2i2−i2i200
χ472-22-22-2-2222-22000-20-22-22-2-222-22-222-2-2000000−i2i2−i2i2i2−i2i2−i200000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000000000000000002-2-22000000−i2i2i2−i200
χ482-22-22-2-2222-22000-20-22-22-2-222-22-222-2-2000000−i2i2−i2i2i2−i2i2−i200000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000000000-222-2000000i2−i2−i2i200
χ492-22-22-2-2222-22000-20-22-22-2-222-22-222-2-2000000i2−i2i2−i2−i2i2−i2i200000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000000000000000002-2-22000000i2−i2−i2i200
χ502-22-22-2-2222-22000-20-22-22-2-222-22-222-2-2000000i2−i2i2−i2−i2i2−i2i200000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000000000-222-2000000−i2i2i2−i200
χ512-2-222-22-2222-2-222-2-2-2-2-2-22222222-2-2-2-20000-2200000000-2-2-2-22222000000000000000000000000000000000000002i2i−2i−2i−2i2i0000000000
χ522-2-222-22-2222-2-222-2-2-2-2-2-22222222-2-2-2-20000-2200000000-2-2-2-2222200000000000000000000000000000000000000−2i−2i2i2i2i−2i0000000000
χ532-2-222-22-22-2-222-2-222-2-2-2-2222-2-2-2-2222222-2-2-220000000022-2-2-2-2220000000000000000-2222-2-20000-2-222000000000000000000000000
χ542-2-222-22-22-2-222-2-222-2-2-2-2222-2-2-2-22222-2-222-220000000022-2-2-2-22200000000000000002-2-2-222000022-2-2000000000000000000000000
χ552-2-222-22-22-2-22-2222-2-2-2-2-2222-2-2-2-2222200002-200000000-2-22222-2-2000000000000000000000000000000000000000000002i−2i−2i2i000000
χ562-2-222-22-22-2-22-2222-2-2-2-2-2222-2-2-2-2222200002-200000000-2-22222-2-200000000000000000000000000000000000000000000−2i2i2i−2i000000
χ572-2-222-22-2-122-22-2-2-221111-1-1-1-1-1-1-1111122-2-22-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii2-2-1-1112i2i−2i−2i-1-111−i−i−i−iiiii0000000000000000
χ582-2-222-22-2-122-22-2-2-221111-1-1-1-1-1-1-1111122-2-22-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i2-2-1-111−2i−2i2i2i-1-111iiii−i−i−i−i0000000000000000
χ592-2-222-22-2-122-22-2-2-221111-1-1-1-1-1-1-11111-2-2222-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-2211-1-1−2i−2i2i2i11-1-1iiii−i−i−i−i0000000000000000
χ602-2-222-22-2-122-22-2-2-221111-1-1-1-1-1-1-11111-2-2222-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-2211-1-12i2i−2i−2i11-1-1−i−i−i−iiiii0000000000000000
χ612-2-222-22-2-1-2-222-2-2221111-1-1-11111-1-1-1-122-2-2-2200000000-1-11111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-22-1-111000011-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ622-2-222-22-2-1-2-222-2-2221111-1-1-11111-1-1-1-122-2-2-2200000000-1-11111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-22-1-111000011-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ632-2-222-22-2-1-2-222-2-2221111-1-1-11111-1-1-1-1-2-222-2200000000-1-11111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-211-1-10000-1-111i3i3−i3−i3−i3−i3i3i30000000000000000
χ642-2-222-22-2-1-2-222-2-2221111-1-1-11111-1-1-1-1-2-222-2200000000-1-11111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-211-1-10000-1-111−i3−i3i3i3i3i3−i3−i30000000000000000
χ652-2-2-2-22222000-2-2202-2-2222-2-2000000002-2-220022−2−2−2−2222-200-220022−2−222−2−2−2−222−2−222002-2-222−2−2200002−22−2−22−220000000000000000
χ662-2-2-2-22222000-2-2202-2-2222-2-2000000002-2-2200−2−22222−2−22-200-2200−2−222−2−22222−2−222−2−2002-2-22−222−20000−22−222−22−20000000000000000
χ672-2-2-2-22222000-2-2202-2-2222-2-200000000-222-20022−2−2−2−2222-200-220022−2−222−2−2−2−222−2−22200-222-2−222−20000−22−222−22−20000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.