Finite Group Databasebeta

← Group #147403

Character table — Group #147403

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order1222444422222244444444444444888888888888888844448888888816161616161616161616161616161616161616161616161616161616161616162244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ9111111111-1-1-11-11-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1-11-1ii−i−i11-1-1ii−i−i
χ10111111111-1-1-11-11-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-11-11−i−iii-1-111−i−iii
χ11111111111-1-1-11-11-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1-11-1−i−iii11-1-1−i−iii
χ12111111111-1-1-11-11-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-11-11ii−i−i-1-111ii−i−i
χ13111111111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1-11-1ii−i−i-1-111−i−iii
χ14111111111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-11-11−i−iii11-1-1ii−i−i
χ15111111111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1-11-1−i−iii-1-111ii−i−i
χ16111111111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-11-11ii−i−i11-1-1−i−iii
χ171111-1-1-1-1-111-1-1-111-1-1iiii−i−i−i−i11iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-111-1-1i−ii−ii−ii−i1-11-1
χ181111-1-1-1-1-111-1-1-111-1-1iiii−i−i−i−i11iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1-1-111−ii−ii−ii−ii-11-11
χ191111-1-1-1-1-111-1-1-111-1-1iiii−i−i−i−i11iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i11-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-1111111-1-1−ii−iii−ii−i-11-11
χ201111-1-1-1-1-111-1-1-111-1-1iiii−i−i−i−i11iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i11-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-1-111i−ii−i−ii−ii1-11-1
χ211111-1-1-1-1-111-1-1-111-1-1−i−i−i−iiiii11−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii11-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-1111111-1-1i−ii−i−ii−ii-11-11
χ221111-1-1-1-1-111-1-1-111-1-1−i−i−i−iiiii11−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii11-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111-1-111−ii−iii−ii−i1-11-1
χ231111-1-1-1-1-111-1-1-111-1-1−i−i−i−iiiii11−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-111-1-1−ii−ii−ii−ii1-11-1
χ241111-1-1-1-1-111-1-1-111-1-1−i−i−i−iiiii11−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1-1-111i−ii−ii−ii−i-11-11
χ251111-1-1-1-1-1-1-11-111-111iiii−i−i−i−i1-1−i−i−i−iiiii-1-111-1-111−i−iiiii−i−i11-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1-11i−i−ii−iii−i
χ261111-1-1-1-1-1-1-11-111-111iiii−i−i−i−i1-1−i−i−i−iiiii-1-111-1-111−i−iiiii−i−i11-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-111-1-111-1−iii−ii−i−ii
χ271111-1-1-1-1-1-1-11-111-111iiii−i−i−i−i1-1−i−i−i−iiiii-1-111-1-111−i−iiiii−i−i11-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11-111-1i−i−iii−i−ii
χ281111-1-1-1-1-1-1-11-111-111iiii−i−i−i−i1-1−i−i−i−iiiii-1-111-1-111−i−iiiii−i−i11-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-111-11-1-11−iii−i−iii−i
χ291111-1-1-1-1-1-1-11-111-111−i−i−i−iiiii1-1iiii−i−i−i−i-1-111-1-111ii−i−i−i−iii11-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-111-1-11−iii−ii−i−ii
χ301111-1-1-1-1-1-1-11-111-111−i−i−i−iiiii1-1iiii−i−i−i−i-1-111-1-111ii−i−i−i−iii11-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-1-111-1i−i−ii−iii−i
χ311111-1-1-1-1-1-1-11-111-111−i−i−i−iiiii1-1iiii−i−i−i−i-1-111-1-111ii−i−i−i−iii11-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11-111-1−iii−i−iii−i
χ321111-1-1-1-1-1-1-11-111-111−i−i−i−iiiii1-1iiii−i−i−i−i-1-111-1-111ii−i−i−i−iii11-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-11-1-11i−i−iii−i−ii
χ332222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ34222222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ35222222222-2-2-22-22-2-2-2222222222-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ36222222222-2-2-22-22-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2-22222222222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ3722222222-222-2-2-2-2-22200000000-2-222-2-222-2-20000000000002-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3822222222-222-2-2-2-2-22200000000-2-222-2-222-2-20000000000002-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3922222222-222-2-2-2-2-22200000000-2-2-2-222-2-222000000000000-22-220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4022222222-222-2-2-2-2-22200000000-2-2-2-222-2-222000000000000-22-220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4122222222-2-2-22-22-22-2-200000000-2222-2-222-2-2000000000000-22-22000022−2−222−2−2−2−222−2−222−2−222−2−22222−2−222−2−20000000000000000
χ4222222222-2-2-22-22-22-2-200000000-2222-2-222-2-2000000000000-22-220000−2−222−2−22222−2−222−2−222−2−222−2−2−2−222−2−2220000000000000000
χ4322222222-2-2-22-22-22-2-200000000-22-2-222-2-2220000000000002-22-2000022−2−222−2−2−2−222−2−22222−2−222−2−2−2−222−2−2220000000000000000
χ4422222222-2-2-22-22-22-2-200000000-22-2-222-2-2220000000000002-22-20000−2−222−2−22222−2−222−2−2−2−222−2−22222−2−222−2−20000000000000000
χ452222-2-2-2-2222222-2-2-2-200000000-2-22i2i−2i−2i−2i−2i2i2i0000000000002i−2i−2i2i000022−2−2−2−22222−2−2−2−222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ462222-2-2-2-2222222-2-2-2-200000000-2-22i2i−2i−2i−2i−2i2i2i0000000000002i−2i−2i2i0000−2−22222−2−2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ472222-2-2-2-2222222-2-2-2-200000000-2-2−2i−2i2i2i2i2i−2i−2i000000000000−2i2i2i−2i000022−2−2−2−22222−2−2−2−222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ482222-2-2-2-2222222-2-2-2-200000000-2-2−2i−2i2i2i2i2i−2i−2i000000000000−2i2i2i−2i0000−2−22222−2−2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ492222-2-2-2-22-2-2-22-2-222200000000-222i2i−2i−2i−2i−2i2i2i000000000000−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−2−22222−2−222−2−2−2−2220000000000000000
χ502222-2-2-2-22-2-2-22-2-222200000000-222i2i−2i−2i−2i−2i2i2i000000000000−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i222−2−2−2−222−2−22222−2−20000000000000000
χ512222-2-2-2-22-2-2-22-2-222200000000-22−2i−2i2i2i2i2i−2i−2i0000000000002i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i222−2−2−2−222−2−22222−2−20000000000000000
χ522222-2-2-2-22-2-2-22-2-222200000000-22−2i−2i2i2i2i2i−2i−2i0000000000002i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−2−22222−2−222−2−2−2−2220000000000000000
χ532222-2-2-2-2-222-2-2-222-2-22i2i2i2i−2i−2i−2i−2i22−2i−2i−2i−2i2i2i2i2i-2-222-2-2222i2i−2i−2i−2i−2i2i2i-2-222000000000000000000000000000000000000000000000000
χ542222-2-2-2-2-222-2-2-222-2-2−2i−2i−2i−2i2i2i2i2i222i2i2i2i−2i−2i−2i−2i-2-222-2-222−2i−2i2i2i2i2i−2i−2i-2-222000000000000000000000000000000000000000000000000
χ552222-2-2-2-2-2-2-22-222-2222i2i2i2i−2i−2i−2i−2i2-22i2i2i2i−2i−2i−2i−2i22-2-222-2-2−2i−2i2i2i−2i−2i2i2i-2-222000000000000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-22-222-222−2i−2i−2i−2i2i2i2i2i2-2−2i−2i−2i−2i2i2i2i2i22-2-222-2-22i2i−2i−2i2i2i−2i−2i-2-222000000000000000000000000000000000000000000000000
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χ652-2-2222-2-2-22-2-222-222-2000000002-2000000002222-2-2-2-2000000002-22-200000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000
χ662-2-2222-2-2-22-2-222-222-2000000002-2000000002222-2-2-2-2000000002-22-20000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000
χ672-2-2222-2-2-22-2-222-222-2000000002-200000000-2-2-2-2222200000000-22-222-2-222-2-222-2-222-2-2200000000000000000000000000000000
χ682-2-2222-2-2-22-2-222-222-2000000002-200000000-2-2-2-2222200000000-22-22-222-2-222-2-222-2-222-200000000000000000000000000000000
χ692-2-2222-2-2-2-2222-2-2-2-220000000022000000002222-2-2-2-200000000-22-222i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ702-2-2222-2-2-2-2222-2-2-2-220000000022000000002222-2-2-2-200000000-22-22−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ712-2-2222-2-2-2-2222-2-2-2-22000000002200000000-2-2-2-22222000000002-22-200000000000000002-2-222-2-22-222-2-222-20000000000000000
χ722-2-2222-2-2-2-2222-2-2-2-22000000002200000000-2-2-2-22222000000002-22-20000000000000000-222-2-222-22-2-222-2-220000000000000000
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χ8944-4-44i−4i4i−4i00000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00004ζ−4ζ004ζ3−4ζ322−222i2−2i222−222i2−2i2000000000000000000000000000000000000000000000000000000000000
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χ974-44-44i−4i−4i4i00000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i004ζ3−4ζ3004ζ−4ζ0022−222i2−2i2−2222−2i22i2000000000000000000000000000000000000000000000000000000000000
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χ1014-44-4−4i4i4i−4i00000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i004ζ−4ζ004ζ3−4ζ300−22222i2−2i222−22−2i22i2000000000000000000000000000000000000000000000000000000000000
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χ1034-44-4−4i4i4i−4i0000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i004ζ−4ζ004ζ3−4ζ30022−22−2i22i2−22222i2−2i2000000000000000000000000000000000000000000000000000000000000
χ1044-44-4−4i4i4i−4i0000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i00−4ζ4ζ00−4ζ34ζ300−22222i2−2i222−22−2i22i2000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.