Finite Group Databasebeta

← Group #129498

Character table — Group #129498

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111111111112222222244444444444444448888888888888888888888888888888888888888888888888888
order1222444488888888224488882244444488888888222244444488888888881616161616161616161616161616161616161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ5111111111111111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ171111-1-1-1-1ii−i−iii−i−i11-1-1i−ii−i1111-1-1-1-1ii−i−iii−i−i1-11-11-11-11-1i−iii−i−iii−i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6
χ181111-1-1-1-1ii−i−iii−i−i11-1-1i−ii−i1111-1-1-1-1ii−i−iii−i−i1-11-11-11-11-1i−iii−i−iii−i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6
χ191111-1-1-1-1ii−i−iii−i−i11-1-1i−ii−i1111-1-1-1-1ii−i−iii−i−i-11-111-1-11-11i−i−i−iii−i−iiiζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6
χ201111-1-1-1-1ii−i−iii−i−i11-1-1i−ii−i1111-1-1-1-1ii−i−iii−i−i-11-111-1-11-11i−i−i−iii−i−iii−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6
χ211111-1-1-1-1ii−i−iii−i−i11-1-1i−ii−i-1-111-1-111−i−iiiii−i−i1-1-11-111-1-11−iiii−i−i−i−iiiζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6
χ221111-1-1-1-1ii−i−iii−i−i11-1-1i−ii−i-1-111-1-111−i−iiiii−i−i1-1-11-111-1-11−iiii−i−i−i−iii−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6
χ231111-1-1-1-1ii−i−iii−i−i11-1-1i−ii−i-1-111-1-111−i−iiiii−i−i-111-1-11-111-1−ii−i−iiiii−i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6
χ241111-1-1-1-1ii−i−iii−i−i11-1-1i−ii−i-1-111-1-111−i−iiiii−i−i-111-1-11-111-1−ii−i−iiiii−i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6
χ251111-1-1-1-1−i−iii−i−iii11-1-1−ii−ii1111-1-1-1-1−i−iii−i−iii1-11-11-11-11-1−ii−i−iii−i−iiiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2
χ261111-1-1-1-1−i−iii−i−iii11-1-1−ii−ii1111-1-1-1-1−i−iii−i−iii1-11-11-11-11-1−ii−i−iii−i−iii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2
χ271111-1-1-1-1−i−iii−i−iii11-1-1−ii−ii1111-1-1-1-1−i−iii−i−iii-11-111-1-11-11−iiii−i−iii−i−iζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2
χ281111-1-1-1-1−i−iii−i−iii11-1-1−ii−ii1111-1-1-1-1−i−iii−i−iii-11-111-1-11-11−iiii−i−iii−i−i−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2
χ291111-1-1-1-1−i−iii−i−iii11-1-1−ii−ii-1-111-1-111ii−i−i−i−iii1-1-11-111-1-11i−i−i−iiiii−i−iζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2
χ301111-1-1-1-1−i−iii−i−iii11-1-1−ii−ii-1-111-1-111ii−i−i−i−iii1-1-11-111-1-11i−i−i−iiiii−i−i−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2
χ311111-1-1-1-1−i−iii−i−iii11-1-1−ii−ii-1-111-1-111ii−i−i−i−iii-111-1-11-111-1i−iii−i−i−i−iiiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2
χ321111-1-1-1-1−i−iii−i−iii11-1-1−ii−ii-1-111-1-111ii−i−i−i−iii-111-1-11-111-1i−iii−i−i−i−iii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2
χ3322222222222222222222222222-2-2-2-2222222-2-2-2-20000-2-20000-2-20000000000000000000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000220000220000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2002-22-20000002-22-2002-20000-220000002-22-200000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2002-22-20000002-22-200-2200002-2000000-22-2200000000000000000000000000000000
χ372222222222222222-2-2-2-2-2-2-2-200-22-22000000-22-222-20000-2200002-22-2000000000000000000000000000000000000
χ382222222222222222-2-2-2-2-2-2-2-200-22-22000000-22-22-2200002-20000-22-22000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-222-2-2-2-222220000-2-20000220000000000000000000000000000000000000000
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χ4222222222-2-2-2-2-2-2-2-2-2-2-2-22222002-22-2000000-22-2200-2200002-20000002-22-200000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-2222200-22-220000002-22-22-20000-220000-22-22000000000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2222200-22-220000002-22-2-2200002-200002-22-2000000000000000000000000000000000000
χ452222-2-2-2-22i2i−2i−2i2i2i−2i−2i22-2-22i−2i2i−2i22-2-222-2-22i2i−2i−2i−2i−2i2i2i0000-220000−2i2i0000000000000000000000000000000000000000
χ462222-2-2-2-22i2i−2i−2i2i2i−2i−2i22-2-22i−2i2i−2i-2-2-2-22222−2i−2i2i2i−2i−2i2i2i00002-200002i−2i0000000000000000000000000000000000000000
χ472222-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-222−2i2i−2i2i002-2-220000002i−2i−2i2i00220000-2-20000002i−2i−2i2i00000000000000000000000000000000
χ482222-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-222−2i2i−2i2i002-2-220000002i−2i−2i2i00-2-2000022000000−2i2i2i−2i00000000000000000000000000000000
χ492222-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-222−2i2i−2i2i00-222-2000000−2i2i2i−2i220000-2-200002i−2i−2i2i000000000000000000000000000000000000
χ502222-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-222−2i2i−2i2i00-222-2000000−2i2i2i−2i-2-20000220000−2i2i2i−2i000000000000000000000000000000000000
χ512222-2-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-2−2i2i−2i2i22-2-222-2-2−2i−2i2i2i2i2i−2i−2i0000-2200002i−2i0000000000000000000000000000000000000000
χ522222-2-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-2−2i2i−2i2i-2-2-2-222222i2i−2i−2i2i2i−2i−2i00002-20000−2i2i0000000000000000000000000000000000000000
χ532222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-2222i−2i2i−2i002-2-22000000−2i2i2i−2i00220000-2-2000000−2i2i2i−2i00000000000000000000000000000000
χ542222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-2222i−2i2i−2i002-2-22000000−2i2i2i−2i00-2-20000220000002i−2i−2i2i00000000000000000000000000000000
χ552222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-2222i−2i2i−2i00-222-20000002i−2i−2i2i220000-2-20000−2i2i2i−2i000000000000000000000000000000000000
χ562222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-2222i−2i2i−2i00-222-20000002i−2i−2i2i-2-200002200002i−2i−2i2i000000000000000000000000000000000000
χ572-2-2222-2-22i2i−2i−2i−2i−2i2i2i2-22-22i−2i−2i2i2-200002-22i−2i2i−2i00000000000000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i
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χ672-2-22-2-2222222-2-2-2-22-2-2222-2-2-2200002-2-222-20000000000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2
χ682-2-22-2-2222222-2-2-2-22-2-2222-2-2-2200002-2-222-20000000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2
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χ702-2-22-2-222-2-2-2-222222-2-22-2-2222-20000-22-222-20000000000000000000000000000000000000000−222−22−2−22−222−22−2−22
χ712-2-22-2-222-2-2-2-222222-2-22-2-222-2200002-22-2-2200000000000000000000000000000000000000002−2−22−222−2−222−22−2−22
χ722-2-22-2-222-2-2-2-222222-2-22-2-222-2200002-22-2-220000000000000000000000000000000000000000−222−22−2−222−2−22−222−2
χ7344-4-44i−4i4i−4i4ζ2−4ζ24ζ6−4ζ64ζ2−4ζ24ζ6−4ζ6000000000000000000000000000000000000000000002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ7000000000000000000000000
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χ7844-4-4−4i4i−4i4i4ζ6−4ζ64ζ2−4ζ24ζ6−4ζ64ζ2−4ζ200000000000000000000000000000000000000000000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ5000000000000000000000000
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χ844-44-44i−4i−4i4i−4ζ64ζ6−4ζ24ζ24ζ6−4ζ64ζ2−4ζ20000000000000000000000000000000000000000000000000000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ50000000000000000
χ854-44-4−4i4i4i−4i4ζ2−4ζ24ζ6−4ζ6−4ζ24ζ2−4ζ64ζ600000000000000000000000000000000000000000000000000002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ30000000000000000
χ864-44-4−4i4i4i−4i4ζ2−4ζ24ζ6−4ζ6−4ζ24ζ2−4ζ64ζ60000000000000000000000000000000000000000000000000000−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ30000000000000000
χ874-44-4−4i4i4i−4i−4ζ24ζ2−4ζ64ζ64ζ2−4ζ24ζ6−4ζ600000000000000000000000000000000000000000000000000002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ70000000000000000
χ884-44-4−4i4i4i−4i−4ζ24ζ2−4ζ64ζ64ζ2−4ζ24ζ6−4ζ60000000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ70000000000000000
χ894-4-4444-4-44i4i−4i−4i−4i−4i4i4i-44-44−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ904-4-4444-4-4−4i−4i4i4i4i4i−4i−4i-44-444i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ914-4-44-4-4444444-4-4-4-4-444-4-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-444-4-4-4-44444-444-444-4-400000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.