Finite Group Databasebeta

← Group #10725798

Character table — Group #10725798

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111111111111222222222222222244444444444488888888888888888888888888888888888812121212121212121212121212121212121212121212121224242424
order1222222222222222366666666666666644444444444444444444121212121212121212121212121212121212121212121212121212124444444444444444444444442244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ41111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ5111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ6111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ1011111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ17111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-111-1-1ii−i−iii−i−i1-1i−ii−i1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i1-11-1
χ18111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-111-1-1ii−i−iii−i−i1-1i−ii−i1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i-1-111−i−iii−i−iii-1-111−i−iii−i−iii-11-11
χ19111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-111-1-1ii−i−i−i−iii-11i−i−ii-1111-1-1ii−i−i−i−iii-1-111-1-111ii−i−i−i−iii11-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii-111-1
χ20111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-111-1-1ii−i−i−i−iii-11i−i−ii-1111-1-1ii−i−i−i−iii-1-111-1-111ii−i−i−i−iii-1-111−i−iiiii−i−i11-1-1−i−iiiii−i−i1-1-11
χ21111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-111-1-1−i−iiiii−i−i-11−iii−i-1111-1-1−i−iiiii−i−i-1-111-1-111−i−iiiii−i−i11-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i-111-1
χ22111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-111-1-1−i−iiiii−i−i-11−iii−i-1111-1-1−i−iiiii−i−i-1-111-1-111−i−iiiii−i−i-1-111ii−i−i−i−iii11-1-1ii−i−i−i−iii1-1-11
χ23111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-111-1-1−i−iii−i−iii1-1−ii−ii1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii11-1-1−i−iii−i−iii1-11-1
χ24111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-111-1-1−i−iii−i−iii1-1−ii−ii1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii-1-111ii−i−iii−i−i-1-111ii−i−iii−i−i-11-11
χ25111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-1-1-111ii−i−iii−i−i-11−ii−ii1-1-1-111ii−i−iii−i−i11-1-1-1-111−i−iii−i−iii11-1-1ii−i−i−i−iii-1-111−i−iiiii−i−i1-1-11
χ26111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-1-1-111ii−i−iii−i−i-11−ii−ii1-1-1-111ii−i−iii−i−i11-1-1-1-111−i−iii−i−iii-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iii-111-1
χ27111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-1-1-111ii−i−i−i−iii1-1−iii−i-11-1-111ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i11-1-1ii−i−iii−i−i11-1-1−i−iii−i−iii-11-11
χ28111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-1-1-111ii−i−i−i−iii1-1−iii−i-11-1-111ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i-1-111−i−iii−i−iii-1-111ii−i−iii−i−i1-11-1
χ29111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-1-1-111−i−iiiii−i−i1-1i−i−ii-11-1-111−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii11-1-1−i−iii−i−iii11-1-1ii−i−iii−i−i-11-11
χ30111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-1-1-111−i−iiiii−i−i1-1i−i−ii-11-1-111−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii-1-111ii−i−iii−i−i-1-111−i−iii−i−iii1-11-1
χ31111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-1-1-111−i−iii−i−iii-11i−ii−i1-1-1-111−i−iii−i−iii11-1-1-1-111ii−i−iii−i−i11-1-1−i−iiiii−i−i-1-111ii−i−i−i−iii1-1-11
χ32111-1-111-1-1-111-1-11-111111-1-1-1-1-1111-1-1-1-1-111−i−iii−i−iii-11i−ii−i1-1-1-111−i−iii−i−iii11-1-1-1-111ii−i−iii−i−i-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i-111-1
χ332222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000
χ342222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1111111111111-1-1-1-111110000000000000000000000000000
χ352222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-22222-2-2-2-222-2-2-1-1-1-11111-1-1-1-1111111111111-1-1-1-10000000000000000000000000000
χ362222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-222-2-2-2-222-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000000000000000000000000000
χ372222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222222222-2-2-2-2-2-2221111-1-1-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000000000
χ382222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-222-2-222-2-21111-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000000000000000
χ392222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222222222-2-2-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000000000000000
χ402222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222111111111111-1-1-1-11111-1-1-1-1-1-1-1-10000000000000000000000000000
χ41222-2-222-2-2-222-2-22-2-1-1-1-1-111111-1-1-111122-2-22i2i−2i−2i2i2i−2i−2i2-22i−2i2i−2i2-2-1-111−i−iii−i−iii-1-111-1-111−i−iii−i−iii0000000000000000000000000000
χ42222-2-222-2-2-222-2-22-2-1-1-1-1-111111-1-1-111122-2-22i2i−2i−2i−2i−2i2i2i-222i−2i−2i2i-22-1-111−i−iiiii−i−i11-1-111-1-1−i−iiiii−i−i0000000000000000000000000000
χ43222-2-222-2-2-222-2-22-2-1-1-1-1-111111-1-1-111122-2-2−2i−2i2i2i2i2i−2i−2i-22−2i2i2i−2i-22-1-111ii−i−i−i−iii11-1-111-1-1ii−i−i−i−iii0000000000000000000000000000
χ44222-2-222-2-2-222-2-22-2-1-1-1-1-111111-1-1-111122-2-2−2i−2i2i2i−2i−2i2i2i2-2−2i2i−2i2i2-2-1-111ii−i−iii−i−i-1-111-1-111ii−i−iii−i−i0000000000000000000000000000
χ45222-2-222-2-2-222-2-22-2-1-1-1-1-111111-1-1-1111-2-2222i2i−2i−2i2i2i−2i−2i-22−2i2i−2i2i2-211-1-1−i−iii−i−iii-1-11111-1-1ii−i−iii−i−i0000000000000000000000000000
χ46222-2-222-2-2-222-2-22-2-1-1-1-1-111111-1-1-1111-2-2222i2i−2i−2i−2i−2i2i2i2-2−2i2i2i−2i-2211-1-1−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii0000000000000000000000000000
χ47222-2-222-2-2-222-2-22-2-1-1-1-1-111111-1-1-1111-2-222−2i−2i2i2i2i2i−2i−2i2-22i−2i−2i2i-2211-1-1ii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i0000000000000000000000000000
χ48222-2-222-2-2-222-2-22-2-1-1-1-1-111111-1-1-1111-2-222−2i−2i2i2i−2i−2i2i2i-222i−2i2i−2i2-211-1-1ii−i−iii−i−i-1-11111-1-1−i−iii−i−iii0000000000000000000000000000
χ4922-2222-2-2-222-2-2-2-22222-2-2222-2-22-2-2-2-222i−2i2i−2i00000000000000002i−2i2i−2i00000000000000000000000000002i−2i2i−2i000000002-22-200000000
χ5022-2222-2-2-222-2-2-2-22222-2-2222-2-22-2-2-2-222i−2i2i−2i00000000000000002i−2i2i−2i0000000000000000000000000000−2i2i−2i2i00000000-22-2200000000
χ5122-2222-2-2-222-2-2-2-22222-2-2222-2-22-2-2-2-22−2i2i−2i2i0000000000000000−2i2i−2i2i00000000000000000000000000002i−2i2i−2i00000000-22-2200000000
χ5222-2222-2-2-222-2-2-2-22222-2-2222-2-22-2-2-2-22−2i2i−2i2i0000000000000000−2i2i−2i2i0000000000000000000000000000−2i2i−2i2i000000002-22-200000000
χ5322-2-2-22-222-22-222-2-2222-2-2-2-2-2222-2-222-22i−2i−2i2i00000000000000002i−2i−2i2i00000000000000000000000000002-2-2200000000−2i2i2i−2i00000000
χ5422-2-2-22-222-22-222-2-2222-2-2-2-2-2222-2-222-22i−2i−2i2i00000000000000002i−2i−2i2i0000000000000000000000000000-222-2000000002i−2i−2i2i00000000
χ5522-2-2-22-222-22-222-2-2222-2-2-2-2-2222-2-222-2−2i2i2i−2i0000000000000000−2i2i2i−2i00000000000000000000000000002-2-22000000002i−2i−2i2i00000000
χ5622-2-2-22-222-22-222-2-2222-2-2-2-2-2222-2-222-2−2i2i2i−2i0000000000000000−2i2i2i−2i0000000000000000000000000000-222-200000000−2i2i2i−2i00000000
χ572-222-2222-22-2-22-2-2-22-2-22-22-2-22-222-22-22000000002-22-200000000000000002-22-200000000000000002i−2i2i−2i00000000000000002i−2i2i−2i0000
χ582-222-2222-22-2-22-2-2-22-2-22-22-2-22-222-22-22000000002-22-200000000000000002-22-20000000000000000−2i2i−2i2i0000000000000000−2i2i−2i2i0000
χ592-222-2222-22-2-22-2-2-22-2-22-22-2-22-222-22-2200000000-22-220000000000000000-22-2200000000000000002i−2i2i−2i0000000000000000−2i2i−2i2i0000
χ602-222-2222-22-2-22-2-2-22-2-22-22-2-22-222-22-2200000000-22-220000000000000000-22-220000000000000000−2i2i−2i2i00000000000000002i−2i2i−2i0000
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χ622-222-2-2-2-22-2222-2-2222-22222-22-2-2-2-2-22-200002-22-200000000000000002-22-20000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ632-222-2-2-2-22-2222-2-2222-22222-22-2-2-2-2-22-20000-22-220000000000000000-22-2200000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
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χ652-22-2222-22-2-2-2-22-222-2-22-2-222-2222-2-22-2000000002i−2i−2i2i00000000000000002i−2i−2i2i00000000000000002i−2i−2i2i0000000000000000-222-20000
χ662-22-2222-22-2-2-2-22-222-2-22-2-222-2222-2-22-2000000002i−2i−2i2i00000000000000002i−2i−2i2i0000000000000000−2i2i2i−2i00000000000000002-2-220000
χ672-22-2222-22-2-2-2-22-222-2-22-2-222-2222-2-22-200000000−2i2i2i−2i0000000000000000−2i2i2i−2i00000000000000002i−2i−2i2i00000000000000002-2-220000
χ682-22-2222-22-2-2-2-22-222-2-22-2-222-2222-2-22-200000000−2i2i2i−2i0000000000000000−2i2i2i−2i0000000000000000−2i2i2i−2i0000000000000000-222-20000
χ692-22-22-2-22-2222-22-2-222-222-2-22-22-2-2-22-2200002i−2i−2i2i00000000000000002i−2i−2i2i00000000000000000000000000002-2-22−2i2i2i−2i000000000000
χ702-22-22-2-22-2222-22-2-222-222-2-22-22-2-2-22-2200002i−2i−2i2i00000000000000002i−2i−2i2i0000000000000000000000000000-222-22i−2i−2i2i000000000000
χ712-22-22-2-22-2222-22-2-222-222-2-22-22-2-2-22-220000−2i2i2i−2i0000000000000000−2i2i2i−2i00000000000000000000000000002-2-222i−2i−2i2i000000000000
χ722-22-22-2-22-2222-22-2-222-222-2-22-22-2-2-22-220000−2i2i2i−2i0000000000000000−2i2i2i−2i0000000000000000000000000000-222-2−2i2i2i−2i000000000000
χ7344444-4-4-4-4-4-4-4444-44-444-44-4444-4-44-4-4-40000000000000000000000000000000000000000000000000000000000000000000000000000
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χ894-444-4444-44-4-44-4-4-4-222-22-222-22-2-22-22-2000000004-44-40000000000000000-22-2200000000000000000000000000000000000000000000
χ904-444-4444-44-4-44-4-4-4-222-22-222-22-2-22-22-200000000-44-4400000000000000002-22-200000000000000000000000000000000000000000000
χ914-444-4-4-4-44-4444-4-44-2-22-2-2-2-22-222222-2200004-44-40000000000000000-22-22000000000000000000000000000000000000000000000000
χ924-444-4-4-4-44-4444-4-44-2-22-2-2-2-22-222222-220000-44-4400000000000000002-22-2000000000000000000000000000000000000000000000000
χ934-44-4444-44-4-4-4-44-44-222-222-2-22-2-2-222-22000000004i−4i−4i4i0000000000000000−2i2i2i−2i00000000000000000000000000000000000000000000
χ944-44-4444-44-4-4-4-44-44-222-222-2-22-2-2-222-2200000000−4i4i4i−4i00000000000000002i−2i−2i2i00000000000000000000000000000000000000000000
χ954-44-44-4-44-4444-44-4-4-2-22-2-222-22-2222-22-200004i−4i−4i4i0000000000000000−2i2i2i−2i000000000000000000000000000000000000000000000000
χ964-44-44-4-44-4444-44-4-4-2-22-2-222-22-2222-22-20000−4i4i4i−4i00000000000000002i−2i−2i2i000000000000000000000000000000000000000000000000
χ974-4-44-44-4-444-44-444-44-4-4-444-4-4-444-44-4440000000000000000000000000000000000000000000000000000000000000000000000000000
χ984-4-44-44-4-444-44-444-4-2222-2-2222-2-22-22-2-200000000000000000000000000000000000000000000−2i32i3−2i32i30000000000000000000000000000
χ994-4-44-44-4-444-44-444-4-2222-2-2222-2-22-22-2-2000000000000000000000000000000000000000000002i3−2i32i3−2i30000000000000000000000000000
χ1004-4-44-4-444-4-44-4-444444-4-4-444-4-44-4444-4-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-44-4-444-4-44-4-4444-2-2222-2-222-22-2-2-222000000000000000000000000000000000000000023−2323−2300000000000000000000000000000000
χ1024-4-44-4-444-4-44-4-4444-2-2222-2-222-22-2-2-2220000000000000000000000000000000000000000−2323−232300000000000000000000000000000000
χ1034-4-4-444-44-4-4-444-4444-4-4-44-4444-44-444-4-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-444-44-4-4-444-444-2222-22-2-2-22-22-2-2220000000000000000000000000000000000000000000023−23−23230000000000000000000000000000
χ1054-4-4-444-44-4-4-444-444-2222-22-2-2-22-22-2-22200000000000000000000000000000000000000000000−232323−230000000000000000000000000000
χ1064-4-4-44-44-4444-44-44-444-4-4-4-4-444-4-444-4440000000000000000000000000000000000000000000000000000000000000000000000000000
χ1074-4-4-44-44-4444-44-44-4-2-222222-2-222-2-22-2-20000000000000000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000
χ1084-4-4-44-44-4444-44-44-4-2-222222-2-222-2-22-2-200000000000000000000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000

Here i is the imaginary unit (i² = −1).