Finite Group Databasebeta

← Group #10801351

Character table — Group #10801351

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size111111111111111122222222222222222222222244444444444444444444444444444444444444446666666688888888888888888888121212121212121212121212121212121212121224242424
order12222222444444443666666688888888121212121212121222444444888888881212121212121212242424242424242424242424242424248888888824666688121212122424242424242424224444444444888888884488
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
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-11111-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ10111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1
χ11111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1
χ12111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-111111111-1-11111-1-1-1-1-1-111
χ13111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1
χ14111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-11111-1-111
χ15111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111
χ16111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1
χ1711111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i-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−iiiii−i−i−i−i1-11111i−i-1-1-1-1ii−i−iii−i−i1111-1-111-1-1-1-1ii−i−iii−i−i1-1i−i
χ1811111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i-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−i−i−i−iiiii1-11111i−i-1-1-1-1ii−i−iii−i−i-1-1-1-111-1-11111−i−iii−i−iii-11−ii
χ1911111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i-1-1-1-1-1-1-1-111-1-111-1-1ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1−ii-1-111ii−i−i−i−iii-1-111-1-111-1-111−i−iiiii−i−i-11−ii
χ2011111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i-1-1-1-1-1-1-1-111-1-111-1-1ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1111-1-1−ii-1-111ii−i−i−i−iii11-1-111-1-111-1-1ii−i−i−i−iii1-1i−i
χ2111111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-1-1-1-1−ii1111−i−iii−i−iii1111-1-1-1-111-1-1ii−i−i−i−iii-11−ii
χ2211111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11-1-1-1-1−ii1111−i−iii−i−iii-1-1-1-11111-1-111−i−iiiii−i−i1-1i−i
χ2311111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111i−i11-1-1−i−iiiii−i−i-1-111-1-1-1-11111−i−iii−i−iii1-1i−i
χ2411111111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-1-111i−i11-1-1−i−iiiii−i−i11-1-11111-1-1-1-1ii−i−iii−i−i-11−ii
χ2511111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiii-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−iiiiiiiii−i−i−i−i1-11111−ii-1-1-1-1−i−iii−i−iii-1-1-1-111-1-11111ii−i−iii−i−i-11i−i
χ2611111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiii-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−i−i−i−iiiii1-11111−ii-1-1-1-1−i−iii−i−iii1111-1-111-1-1-1-1−i−iii−i−iii1-1−ii
χ2711111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiii-1-1-1-1-1-1-1-111-1-111-1-1−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1111-1-1i−i-1-111−i−iiiii−i−i11-1-111-1-111-1-1−i−iiiii−i−i1-1−ii
χ2811111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiii-1-1-1-1-1-1-1-111-1-111-1-1−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1111-1-1i−i-1-111−i−iiiii−i−i-1-111-1-111-1-111ii−i−i−i−iii-11i−i
χ2911111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11-1-1-1-1i−i1111ii−i−iii−i−i-1-1-1-11111-1-111ii−i−i−i−iii1-1−ii
χ3011111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-1-1-1-1i−i1111ii−i−iii−i−i1111-1-1-1-111-1-1−i−iiiii−i−i-11i−i
χ3111111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-1-1-111−ii11-1-1ii−i−i−i−iii11-1-11111-1-1-1-1−i−iii−i−iii-11i−i
χ3211111111-1-1-1-1-1-1-1-111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-1-111−ii11-1-1ii−i−i−i−iii-1-111-1-1-1-11111ii−i−iii−i−i1-1−ii
χ332222222222222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ342222222222222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-2-2-2-2222222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000-2-2-1-111-2-2-1-111-1-1-1-11111000000000000000000000000
χ352222222222222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-21111-2-2111111111111000000000000000000000000
χ362222222222222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-111111111000000002211-1-12211-1-11111-1-1-1-1000000000000000000000000
χ372222222222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000022-1-1-1-1-2-2-1-1-1-111111111000000000000000000000000
χ382222222222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000-2-2-1-11122-1-1111111-1-1-1-1000000000000000000000000
χ392222222222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-22222-2-22222-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000-2-21111221111-1-1-1-1-1-1-1-1000000000000000000000000
χ402222222222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222222221111111111111111-1-1-1-1-1-1-1-1000000002211-1-1-2-211-1-1-1-1-1-11111000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-12i2i2i2i−2i−2i−2i−2i111111112222-2-2-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii000000002-2-1-1-1-12i−2i1111−i−iii−i−iii000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-12i2i2i2i−2i−2i−2i−2i1111111122-2-222-2-22i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000-22-1-111−2i2i11-1-1−i−iiiii−i−i000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-12i2i2i2i−2i−2i−2i−2i11111111-2-222-2-222−2i−2i2i2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii00000000-221111−2i2i-1-1-1-1ii−i−iii−i−i000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-12i2i2i2i−2i−2i−2i−2i11111111-2-2-2-22222−2i−2i2i2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i000000002-211-1-12i−2i-1-111ii−i−i−i−iii000000000000000000000000
χ4522222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1−2i−2i−2i−2i2i2i2i2i111111112222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i000000002-2-1-1-1-1−2i2i1111ii−i−iii−i−i000000000000000000000000
χ4622222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1−2i−2i−2i−2i2i2i2i2i1111111122-2-222-2-2−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000-22-1-1112i−2i11-1-1ii−i−i−i−iii000000000000000000000000
χ4722222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1−2i−2i−2i−2i2i2i2i2i11111111-2-222-2-2222i2i−2i−2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i00000000-2211112i−2i-1-1-1-1−i−iii−i−iii000000000000000000000000
χ4822222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1−2i−2i−2i−2i2i2i2i2i11111111-2-2-2-222222i2i−2i−2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii000000002-211-1-1−2i2i-1-111−i−iiiii−i−i000000000000000000000000
χ49222-2-22-2-222-2-2-2-222222-2-2-2-222i2i−2i−2i2i2i−2i−2i2222-2-2-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000022-2-222-2-200000000000000000000002i−2i2i−2i000000000000000000
χ50222-2-22-2-222-2-2-2-222222-2-2-2-222i2i−2i−2i2i2i−2i−2i2222-2-2-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000-2-222-2-2220000000000000000000000−2i2i−2i2i000000000000000000
χ51222-2-22-2-222-2-2-2-222222-2-2-2-22−2i−2i2i2i−2i−2i2i2i2222-2-2-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000022-2-222-2-20000000000000000000000−2i2i−2i2i000000000000000000
χ52222-2-22-2-222-2-2-2-222222-2-2-2-22−2i−2i2i2i−2i−2i2i2i2222-2-2-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000-2-222-2-22200000000000000000000002i−2i2i−2i000000000000000000
χ53222-2-22-2-2-2-22222-2-2222-2-2-2-2222-2-2-2-222-2-2-2-2222200000000000000000000000022-2-2-2-222000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000−2i2i2i−2i000000000000000000
χ54222-2-22-2-2-2-22222-2-2222-2-2-2-2222-2-2-2-222-2-2-2-2222200000000000000000000000022-2-2-2-22200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000002i−2i−2i2i000000000000000000
χ55222-2-22-2-2-2-22222-2-2222-2-2-2-22-2-22222-2-2-2-2-2-22222000000000000000000000000-2-22222-2-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000002i−2i−2i2i000000000000000000
χ56222-2-22-2-2-2-22222-2-2222-2-2-2-22-2-22222-2-2-2-2-2-22222000000000000000000000000-2-22222-2-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000−2i2i2i−2i000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.