Finite Group Databasebeta

← Group #12007612

Character table — Group #12007612

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140
size1111111122222222222222222222222222224444444444444444444444448888888888888888888888888888888888888888888888888888888888882020202020202020404040404040404040404040
order1222222222224444444455101010101010101010101010101010101010101010102020202020202020202020202020202044444444888820202020202020202020202020202020202020202020202020202020202020204040404040404040404040404040404044444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91-11-1-111-11-1-11111-1-1-11-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111i−iii−i−ii−i11-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−i
χ101-11-1-111-11-1-11111-1-1-11-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111i−iii−i−ii−i11-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iii−i−iii
χ111-11-1-111-11-1-11111-1-1-11-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111i−i−i−iiii−i-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111−i−iiiii−i−i
χ121-11-1-111-11-1-11111-1-1-11-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111i−i−i−iiii−i-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1ii−i−i−i−iii
χ131-11-1-111-11-1-11111-1-1-11-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111−iiii−i−i−ii-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111ii−i−i−i−iii
χ141-11-1-111-11-1-11111-1-1-11-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111−iiii−i−i−ii-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1−i−iiiii−i−i
χ151-11-1-111-11-1-11111-1-1-11-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111−ii−i−iii−ii11-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii
χ161-11-1-111-11-1-11111-1-1-11-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111−ii−i−iii−ii11-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−iii−i−i
χ1722222222222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−52222222222222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200000000000000000000
χ1822222222222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−5222-2-2-2-222-2-2-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5200000000000000000000
χ1922222222222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−52-2-22222-2-2-2-2-2-21−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5200000000000000000000
χ2022222222222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−52-2-2-2-2-2-2-2-222221−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200000000000000000000
χ2122222222222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52222222222222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000000000000000000
χ2222222222222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+5222-2-2-2-222-2-2-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5200000000000000000000
χ2322222222222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52-2-22222-2-2-2-2-2-21+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5200000000000000000000
χ2422222222222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52-2-2-2-2-2-2-2-222221+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000000000000000000
χ25222222222222-2-2-2-2-2-2-2-2222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000000000000000000000000000002-22-20000
χ26222222222222-2-2-2-2-2-2-2-2222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000000000000000000000000000-22-220000
χ2722222222-2-2-2-222-22-2-2-222222222222222222-2-2-2-2-2-2-2-222-222-222-2-222-2-2-2-2000000000000000000000000000000000000000000000000000000000000000000002-22-200000000
χ2822222222-2-2-2-222-22-2-2-222222222222222222-2-2-2-2-2-2-2-222-222-222-2-222-2-2-2-200000000000000000000000000000000000000000000000000000000000000000000-22-2200000000
χ2922222222-2-2-2-2-2-22-2222-22222222222222222-2-2-2-2-2-2-2-2-2-22-2-22-2-222-2-22222220000-2-2000022-2-222-2-222-2-222-2-20000000000000000000000000000000000000000000000000000
χ3022222222-2-2-2-2-2-22-2222-22222222222222222-2-2-2-2-2-2-2-2-2-22-2-22-2-222-2-22222-2-20000220000-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ3122222222-2-2-2-2-2-22-2222-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−52−1+521+521+52−1−521−521−52−1+52−1+521+521+52−1−52−1−52−1+52−1−52220000-2-20000−1+52−1+521−521−52−1−52−1−521+521+52−1+52−1+521−521−52−1−52−1−521+521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ1800000000000000000000
χ3222222222-2-2-2-2-2-22-2222-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−52−1+521+521+52−1−521−521−52−1+52−1+521+521+52−1−52−1−52−1+52−1−52220000-2-20000−1+52−1+521−521−52−1−52−1−521+521+52−1+52−1+521−521−52−1−52−1−521+521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ1800000000000000000000
χ3322222222-2-2-2-2-2-22-2222-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−52−1+521+521+52−1−521−521−52−1+52−1+521+521+52−1−52−1−52−1+52−1−52-2-200002200001−521−52−1+52−1+521+521+52−1−52−1−521−521−52−1+52−1+521+521+52−1−52−1−52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ1800000000000000000000
χ3422222222-2-2-2-2-2-22-2222-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−52−1+521+521+52−1−521−521−52−1+52−1+521+521+52−1−52−1−52−1+52−1−52-2-200002200001−521−52−1+52−1+521+521+52−1−52−1−521−521−52−1+52−1+521+521+52−1−52−1−52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ1800000000000000000000
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Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.