Finite Group Databasebeta

← Group #13021689

Character table — Group #13021689

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111222222224444444444444444444444444455555555888888888888888888888888101010101010101020202020202020202020202020202020202020202020202020204040404040404040
order12222222222244444458888888810101010101010202020202020202022222222101010102020202040404040404040404040404040404040222244444444444444444444448888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111−i−i−i−iiiii
χ81111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111iiii−i−i−i−i
χ911111111-1-1-1-11111-1-111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1111111111-1-1-1-11111-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iii
χ1211111111-1-1-1-11111-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iiiii−i−i
χ1311111111-1-1-1-11111-1-11-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1411111111-1-1-1-11111-1-11-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1511111111-1-1-1-11111-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−i−iiiii−i−i
χ1611111111-1-1-1-11111-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1ii−i−i−i−iii
χ17111-1-1-1-1111-1-111-1-11-11ii−i−iii−i−i11-1-1-1-111111-1-1-1-1111-1-1-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-11-111-1-111-1-111-1-111-1-1ii−i−iii−i−ii−ii−ii−ii−i
χ18111-1-1-1-1111-1-111-1-11-11ii−i−iii−i−i11-1-1-1-111111-1-1-1-1111-1-1-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-11-1-1-111-1-111-1-111-1-111ii−i−iii−i−i−ii−ii−ii−ii
χ19111-1-1-1-1111-1-111-1-11-11ii−i−iii−i−i11-1-1-1-111111-1-1-1-1-1-1-11111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111-11ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-11-111-11-1
χ20111-1-1-1-1111-1-111-1-11-11ii−i−iii−i−i11-1-1-1-111111-1-1-1-1-1-1-11111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111-11−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii1-11-1-11-11
χ21111-1-1-1-1111-1-111-1-11-11−i−iii−i−iii11-1-1-1-111111-1-1-1-1111-1-1-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-11-111-1-111-1-111-1-111-1-1−i−iii−i−iii−ii−ii−ii−ii
χ22111-1-1-1-1111-1-111-1-11-11−i−iii−i−iii11-1-1-1-111111-1-1-1-1111-1-1-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-11-1-1-111-1-111-1-111-1-111−i−iii−i−iiii−ii−ii−ii−i
χ23111-1-1-1-1111-1-111-1-11-11−i−iii−i−iii11-1-1-1-111111-1-1-1-1-1-1-11111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111-11ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i1-11-1-11-11
χ24111-1-1-1-1111-1-111-1-11-11−i−iii−i−iii11-1-1-1-111111-1-1-1-1-1-1-11111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111-11−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-11-111-11-1
χ25111-1-1-1-11-1-11111-1-1-111ii−i−i−i−iii11-1-1-1-111111-1-1-1-1111-1-1-1-11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1-1111-1-1-1-11111-1-1-1-111ii−i−i−i−iiii−i−iii−i−ii
χ26111-1-1-1-11-1-11111-1-1-111ii−i−i−i−iii11-1-1-1-111111-1-1-1-1111-1-1-1-11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1-11-1-11111-1-1-1-11111-1-1ii−i−i−i−iii−iii−i−iii−i
χ27111-1-1-1-11-1-11111-1-1-111ii−i−i−i−iii11-1-1-1-111111-1-1-1-1-1-1-11111-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1111-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-111-11-1-11
χ28111-1-1-1-11-1-11111-1-1-111ii−i−i−i−iii11-1-1-1-111111-1-1-1-1-1-1-11111-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1111-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-11-111-1
χ29111-1-1-1-11-1-11111-1-1-111−i−iiiii−i−i11-1-1-1-111111-1-1-1-1111-1-1-1-11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1-1111-1-1-1-11111-1-1-1-111−i−iiiii−i−i−iii−i−iii−i
χ30111-1-1-1-11-1-11111-1-1-111−i−iiiii−i−i11-1-1-1-111111-1-1-1-1111-1-1-1-11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1-11-1-11111-1-1-1-11111-1-1−i−iiiii−i−ii−i−iii−i−ii
χ31111-1-1-1-11-1-11111-1-1-111−i−iiiii−i−i11-1-1-1-111111-1-1-1-1-1-1-11111-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1111-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-11-111-1
χ32111-1-1-1-11-1-11111-1-1-111−i−iiiii−i−i11-1-1-1-111111-1-1-1-1-1-1-11111-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1111-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-111-11-1-11
χ33222222222222-2-2-2-2-2-22000000002222222-2-2-2-2-2-2-2-2222222222222-2-2-2-200000000000000002222-2-2-2-2-2-200000000000000000000000000000000
χ34222222222222-2-2-2-2-2-22000000002222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-2-2-222222200000000000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-2222000000002222222-2-2-2-2-2-2-2-222222222-2-2-2-222220000000000000000-2-2-2-2-2-2-2-22200000000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-2222000000002222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000022222222-2-200000000000000000000000000000000
χ37222-2-2-2-2222-2-2-2-222-2220000000022-2-2-2-22-2-2-2-22222222-2-2-2-2222-2-2-2-222000000000000000022-2-2-2-222-2200000000000000000000000000000000
χ38222-2-2-2-2222-2-2-2-222-2220000000022-2-2-2-22-2-2-2-22222-2-2-22222-222-2-2-2-2220000000000000000-2-22222-2-22-200000000000000000000000000000000
χ39222-2-2-2-22-2-222-2-2222-220000000022-2-2-2-22-2-2-2-22222222-2-2-2-22-2-22222-2-20000000000000000-2-222-2-2222-200000000000000000000000000000000
χ40222-2-2-2-22-2-222-2-2222-220000000022-2-2-2-22-2-2-2-22222-2-2-22222-2-2-22222-2-2000000000000000022-2-222-2-2-2200000000000000000000000000000000
χ4122-222-2-2-22-22-20000002i2−i2i2−i2i2−i2i2−i22-222-2-2-20000000022-2-2-222-22-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-22-20000000000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ4222-222-2-2-22-22-20000002i2−i2i2−i2i2−i2i2−i22-222-2-2-200000000-2-2222-2-222-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-22-220000000000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ4322-222-2-2-22-22-20000002−i2i2−i2i2−i2i2−i2i22-222-2-2-20000000022-2-2-222-22-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-22-20000000000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ4422-222-2-2-22-22-20000002−i2i2−i2i2−i2i2−i2i22-222-2-2-200000000-2-2222-2-222-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-22-220000000000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ4522-222-2-2-2-22-220000002i2−i2i2−i2−i2i2−i2i22-222-2-2-20000000022-2-2-222-2-22-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ4622-222-2-2-2-22-220000002i2−i2i2−i2−i2i2−i2i22-222-2-2-200000000-2-2222-2-22-22-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22-22-20000000000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ4722-222-2-2-2-22-220000002−i2i2−i2i2i2−i2i2−i22-222-2-2-20000000022-2-2-222-2-22-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ4822-222-2-2-2-22-220000002−i2i2−i2i2i2−i2i2−i22-222-2-2-200000000-2-2222-2-22-22-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22-22-20000000000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ4922-2-2-222-22-2-2200000022−2−222−2−222-2-2-222-20000000022-222-2-2-22-2-22000022−2−2−2−22222−2−2−2−2222-2-2200000000000000000000002−2−222−2−2200000000
χ5022-2-2-222-22-2-2200000022−2−222−2−222-2-2-222-200000000-2-22-2-22222-2-22000022−2−2−2−22222−2−2−2−222-222-20000000000000000000000−222−2−222−200000000
χ5122-2-2-222-22-2-220000002−222−2−222−22-2-2-222-20000000022-222-2-2-22-2-220000−2−22222−2−2−2−22222−2−22-2-220000000000000000000000−222−2−222−200000000
χ5222-2-2-222-22-2-220000002−222−2−222−22-2-2-222-200000000-2-22-2-22222-2-220000−2−22222−2−2−2−22222−2−2-222-200000000000000000000002−2−222−2−2200000000
χ5322-2-2-222-2-222-200000022−2−22−222−22-2-2-222-20000000022-222-2-2-2-222-2000022−2−2−2−222−2−22222−2−2-222-200000000000000000000002−2−22−222−200000000
χ5422-2-2-222-2-222-200000022−2−22−222−22-2-2-222-200000000-2-22-2-2222-222-2000022−2−2−2−222−2−22222−2−22-2-220000000000000000000000−222−22−2−2200000000
χ5522-2-2-222-2-222-20000002−222−22−2−222-2-2-222-20000000022-222-2-2-2-222-20000−2−22222−2−222−2−2−2−222-222-20000000000000000000000−222−22−2−2200000000
χ5622-2-2-222-2-222-20000002−222−22−2−222-2-2-222-200000000-2-22-2-2222-222-20000−2−22222−2−222−2−2−2−2222-2-2200000000000000000000002−2−22−222−200000000
χ572-2-22-22-2200002-22-200200000000-2-22-22-2222-2-222-2-22-222-22-2-200000000000000000000000000002-22-20000002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ582-2-22-22-2200002-22-200200000000-2-22-22-2222-2-222-2-22-222-22-2-200000000000000000000000000002-22-2000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
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χ652-2-2-22-22200002-2-2200200000000-2-2-22-22222-2-2-2-2222-22-22-22-200000000000000000000000000002-2-220000002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ662-2-2-22-22200002-2-2200200000000-2-2-22-22222-2-2-2-2222-22-22-22-200000000000000000000000000002-2-22000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ672-2-2-22-22200002-2-2200200000000-2-2-22-22222-2-2-2-222-22-22-22-220000000000000000000000000000-222-20000002-2-220000-222-20000000000000000
χ682-2-2-22-22200002-2-2200200000000-2-2-22-22222-2-2-2-222-22-22-22-220000000000000000000000000000-222-2000000-222-200002-2-220000000000000000
χ692-2-2-22-2220000-222-200200000000-2-2-22-222-2-22222-2-22-22-22-22-20000000000000000000000000000-222-2002i−2i−2i2i00002i−2i−2i2i00000000000000000000
χ702-2-2-22-2220000-222-200200000000-2-2-22-222-2-22222-2-22-22-22-22-20000000000000000000000000000-222-200−2i2i2i−2i0000−2i2i2i−2i00000000000000000000
χ712-2-2-22-2220000-222-200200000000-2-2-22-222-2-22222-2-2-22-22-22-2200000000000000000000000000002-2-22002-2-220000-222-200000000000000000000
χ722-2-2-22-2220000-222-200200000000-2-2-22-222-2-22222-2-2-22-22-22-2200000000000000000000000000002-2-2200-222-200002-2-2200000000000000000000
χ73444444444444444444-144444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ74444444444444444444-1-4-4-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-11111111111111111000000000000000000000000000000000000000000
χ75444444444444-4-4-4-4-4-4-100000000-1-1-1-1-1-1-11111111100000000-1-1-1-11111i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5000000000000000000000000000000000000000000
χ76444444444444-4-4-4-4-4-4-100000000-1-1-1-1-1-1-11111111100000000-1-1-1-11111−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5000000000000000000000000000000000000000000
χ7744444444-4-4-4-44444-4-4-14444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011111111-1-1-1-1-1-1-1-111111111000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.