Finite Group Databasebeta

← Group #10800190

Character table — Group #10800190

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size111111111111111122222222222222222222222244444444444444444444444444444444444444446666666688888888888888888888121212121212121212121212121212121212121224242424
order12222222444444443444444446666666121212121212121222224444888888881212121212121212242424242424242424242424242424244444444466668888121212122424242424242424224444444444888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1
χ911111111111111111-1-1-1-1-1-1-1-111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111111111111-1-1-1-1-1-1-1-111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ1111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1211111111111111111-1-1-1-1-1-1-1-111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ1411111111111111111-1-1-1-1-1-1-1-1111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1
χ1511111111111111111-1-1-1-1-1-1-1-1111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ1611111111111111111-1-1-1-1-1-1-1-1111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ1711111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111i−ii−i-1-1-1-1ii−i−iii−i−i11-1-111-1-111-1-1ii−i−iii−i−ii−ii−i
χ1811111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111111111i−ii−i-1-1-1-1ii−i−iii−i−i-1-111-1-111-1-111−i−iii−i−iii−ii−ii
χ1911111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111−ii−ii-1-1-1-1−i−iii−i−iii11-1-111-1-111-1-1−i−iii−i−iii−ii−ii
χ2011111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111111111−ii−ii-1-1-1-1−i−iii−i−iii-1-111-1-111-1-111ii−i−iii−i−ii−ii−i
χ2111111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-1−ii−ii1111−i−iii−i−iii11-1-1-1-111-1-111ii−i−iii−i−i−ii−ii
χ2211111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-1−ii−ii1111−i−iii−i−iii-1-11111-1-111-1-1−i−iii−i−iiii−ii−i
χ2311111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-1i−ii−i1111ii−i−iii−i−i11-1-1-1-111-1-111−i−iii−i−iiii−ii−i
χ2411111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-1i−ii−i1111ii−i−iii−i−i-1-11111-1-111-1-1ii−i−iii−i−i−ii−ii
χ2511111111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-111-1-1i−i−ii-1-111ii−i−i−i−iii-1-11111-1-1-1-111ii−i−i−i−iiii−i−ii
χ2611111111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1i−i−ii-1-111ii−i−i−i−iii11-1-1-1-11111-1-1−i−iiiii−i−i−iii−i
χ2711111111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-111-1-1−iii−i-1-111−i−iiiii−i−i-1-11111-1-1-1-111−i−iiiii−i−i−iii−i
χ2811111111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1−iii−i-1-111−i−iiiii−i−i11-1-1-1-11111-1-1ii−i−i−i−iiii−i−ii
χ2911111111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111−iii−i11-1-1−i−iiiii−i−i-1-111-1-11111-1-1ii−i−i−i−iii−iii−i
χ3011111111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111−iii−i11-1-1−i−iiiii−i−i11-1-111-1-1-1-111−i−iiiii−i−ii−i−ii
χ3111111111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111i−i−ii11-1-1ii−i−i−i−iii-1-111-1-11111-1-1−i−iiiii−i−ii−i−ii
χ3211111111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-111i−i−ii11-1-1ii−i−i−i−iii11-1-111-1-1-1-111ii−i−i−i−iii−iii−i
χ332222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ342222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000000000000000
χ352222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000001111-2-2-2-2111111111111000000000000000000000000
χ362222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000111122221111-1-1-1-1-1-1-1-1000000000000000000000000
χ372222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000-1-11122-2-2-1-111-1-1-1-11111000000000000000000000000
χ382222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000-1-111-2-222-1-1111111-1-1-1-1000000000000000000000000
χ392222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2222222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000011-1-1-2-22211-1-11111-1-1-1-1000000000000000000000000
χ402222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000011-1-122-2-211-1-1-1-1-1-11111000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii00000000-1-1-1-12i−2i2i−2i1111−i−iii−i−iii000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i00000000-1-1-1-1−2i2i−2i2i1111ii−i−iii−i−i000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-222222i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii000000001111−2i2i−2i2i-1-1-1-1ii−i−iii−i−i000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-22222−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i0000000011112i−2i2i−2i-1-1-1-1−i−iii−i−iii000000000000000000000000
χ4522222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-11111111122-2-2-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000-1-1112i−2i−2i2i11-1-1−i−iiiii−i−i000000000000000000000000
χ4622222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-11111111122-2-2-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000-1-111−2i2i2i−2i11-1-1ii−i−i−i−iii000000000000000000000000
χ4722222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-22222-2-22i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000011-1-1−2i2i2i−2i-1-111ii−i−i−i−iii000000000000000000000000
χ4822222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-22222-2-2−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000011-1-12i−2i−2i2i-1-111−i−iiiii−i−i000000000000000000000000
χ49222-2-22-2-22222-2-2-2-220000000022-2-2-2-22-2-222-2-2220000000000002-22-2000000000000000022-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000002i−2i2i−2i0000
χ50222-2-22-2-22222-2-2-2-220000000022-2-2-2-22-2-222-2-2220000000000002-22-2000000000000000022-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000−2i2i−2i2i0000
χ51222-2-22-2-22222-2-2-2-220000000022-2-2-2-22-2-222-2-222000000000000-22-220000000000000000-2-222-2-2222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000−2i2i−2i2i0000
χ52222-2-22-2-22222-2-2-2-220000000022-2-2-2-22-2-222-2-222000000000000-22-220000000000000000-2-222-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000002i−2i2i−2i0000
χ53222-2-22-2-2-2-2-2-2222220000000022-2-2-2-2222-2-222-2-20000000000002i−2i−2i2i00000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000-222-20000
χ54222-2-22-2-2-2-2-2-2222220000000022-2-2-2-2222-2-222-2-20000000000002i−2i−2i2i00000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000002-2-220000
χ55222-2-22-2-2-2-2-2-2222220000000022-2-2-2-2222-2-222-2-2000000000000−2i2i2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000002-2-220000
χ56222-2-22-2-2-2-2-2-2222220000000022-2-2-2-2222-2-222-2-2000000000000−2i2i2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000-222-20000
χ5722-22-2-22-22i−2i2i−2i2i−2i2i−2i222-2-22i2i−2i−2i2-22-22-2-22i−2i2i−2i2i−2i2i−2i000000000000000022-2-22i2i−2i−2i0000000000000000000000000000000000000000000000002-22i−2i2-22i−2i000000000000
χ5822-22-2-22-22i−2i2i−2i2i−2i2i−2i222-2-22i2i−2i−2i2-22-22-2-22i−2i2i−2i2i−2i2i−2i000000000000000022-2-22i2i−2i−2i000000000000000000000000000000000000000000000000-22−2i2i-22−2i2i000000000000
χ5922-22-2-22-22i−2i2i−2i2i−2i2i−2i2-2-222−2i−2i2i2i2-22-22-2-22i−2i2i−2i2i−2i2i−2i0000000000000000-2-222−2i−2i2i2i0000000000000000000000000000000000000000000000002-22i−2i-22−2i2i000000000000
χ6022-22-2-22-22i−2i2i−2i2i−2i2i−2i2-2-222−2i−2i2i2i2-22-22-2-22i−2i2i−2i2i−2i2i−2i0000000000000000-2-222−2i−2i2i2i000000000000000000000000000000000000000000000000-22−2i2i2-22i−2i000000000000
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χ1234-444-4-4-44−4i4i4i−4i−4i4i4i−4i-2000000002-2-222-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ232ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000000000000000000000000000
χ1244-444-4-4-44−4i4i4i−4i−4i4i4i−4i-2000000002-2-222-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000002ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ23−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000000000000000000000000000
χ1254-4-4444-4-444-4-444-4-4-20000000022-2-222-22222-2-2-2-2000000004-44-4000000000000-22-22-22-22000000000000000000000000000000000000000000000000000000000000
χ1264-4-4444-4-444-4-444-4-4-20000000022-2-222-22222-2-2-2-200000000-44-440000000000002-22-22-22-2000000000000000000000000000000000000000000000000000000000000
χ1274-4-4444-4-4-4-444-4-444-20000000022-2-222-2-2-2-2-22222000000004i−4i−4i4i000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000000000000000
χ1284-4-4444-4-4-4-444-4-444-20000000022-2-222-2-2-2-2-2222200000000−4i4i4i−4i0000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000000000000000
χ1294-4-4-4-444444-4-4-4-444-24-4-444-4-442222-2-2-2-2-22222-2-20000000000000000-222-2-222-200000000000000000000000000000000000000000000000000000000000000000000
χ1304-4-4-4-444444-4-4-4-444-2-444-4-444-42222-2-2-2-2-22222-2-200000000000000002-2-222-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1314-4-4-4-4444-4-44444-4-4-24-4-44-444-42222-2-2-222-2-2-2-2220000000000000000-222-22-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1324-4-4-4-4444-4-44444-4-4-2-444-44-4-442222-2-2-222-2-2-2-22200000000000000002-2-22-222-200000000000000000000000000000000000000000000000000000000000000000000

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