Finite Group Databasebeta

← Group #205641

Character table — Group #205641

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12224444222244444444444444448888888888888888244488888888888888888888888888888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111−i−iii−i−iii
χ1111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-1−i−iii−i−iii
χ1211111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111ii−i−iii−i−i
χ1311111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1-11-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-11-1111-1-1−i−iiiii−i−i
χ1511111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1-11-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-11-1111-1-1ii−i−i−i−iii
χ171111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-1-111-11-1i−ii−ii−ii−i
χ181111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-111-1-11-11−ii−ii−ii−ii
χ191111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-1-111-11-1−ii−ii−ii−ii
χ201111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-111-1-11-11i−ii−ii−ii−i
χ211111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-11-11-11i−ii−i−ii−ii
χ221111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-111-11-11-1−ii−iii−ii−i
χ231111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-1-11-11-11−ii−iii−ii−i
χ241111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-111-11-11-1i−ii−i−ii−ii
χ251111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-111-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-1-111-1-111-1-11
χ261111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-111-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-111-1-111-1-111-1
χ271111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-111-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-1-11-111-1-111-1
χ281111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-111-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-111-11-1-111-1-11
χ291111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-111-11-1-11-111-1
χ301111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111-1-11-111-11-1-11
χ311111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1-111-11-1-11
χ321111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-111-1-11-111-1
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χ34222222222222-2-222-2-2-2-2-2-222-2-2-2-2000000000000000022-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ352222222222-2-222-2-222-2-2222222-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ362222222222-2-222-2-222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ372222222222-2-2-2-2-2-2-2-222-2-222-2-2220000000000000000-2-2220000000022-2-222-2-222-2-222-2-200000000000000000000000000000000
χ382222222222-2-2-2-2-2-2-2-222-2-222-2-2220000000000000000-2-22200000000-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ3922222222-2-2222222-2-22222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ4022222222-2-2222222-2-22222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ4122222222-2-222-2-22222-2-2-2-2-2-222-2-20000000000000000-2-222000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ4222222222-2-222-2-22222-2-2-2-2-2-222-2-20000000000000000-2-22200000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000022-2-200000000000000000000000022-2-222-2-2-2-222-2-2220000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000022-2-2000000000000000000000000-2-222-2-22222-2-222-2-20000000000000000
χ452222-2-2-2-2222222-2-2-2-222-2-2-2-222-2-200000000000000002-22-2000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ462222-2-2-2-2222222-2-2-2-222-2-2-2-222-2-200000000000000002-22-200000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ472222-2-2-2-22222-2-2-2-222-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-22-2-22-2-222-2-222000000000000000000000000000000000000000000000000
χ482222-2-2-2-22222-2-2-2-222-2-222-2-2-2-222-2-2-2-22222-2-2-2-222222-2-2222-2-222-2-2000000000000000000000000000000000000000000000000
χ492222-2-2-2-222-2-22222-2-2-2-2-2-2-2-222220000000000000000-22-2200000000000000000000000022-2-2-2-22222-2-2-2-2220000000000000000
χ502222-2-2-2-222-2-22222-2-2-2-2-2-2-2-222220000000000000000-22-22000000000000000000000000-2-22222-2-2-2-22222-2-20000000000000000
χ512222-2-2-2-2-2-22222-2-22222-2-222-2-2-2-20000000000000000-22-220000000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ522222-2-2-2-2-2-22222-2-22222-2-222-2-2-2-20000000000000000-22-22000000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ532222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-22200000000000000002-22-20000000022-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ542222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-22200000000000000002-22-200000000-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ552222-2-2-2-2-2-2-2-2-2-222-2-222222222-2-22222-2-2-2-2-2-2-2-222222-2-22-2-22222-2-2000000000000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-2-2-222-2-222222222-2-2-2-2-2-222222222-2-2-2-22-2-2222-2-2-2-222000000000000000000000000000000000000000000000000
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χ6922-2-22i2i−2i−2i00-22−2i2i−2i2i002i−2i-2200002-22i2i−2i−2i22-2-20000000000000000-22−2i2ii2−i2−i2i22−2−222−2−22i2−i2−i2i2−222−2−i2i2i2−i2i2−i2−i2i22−2−220000000000000000
χ7022-2-22i2i−2i−2i00-22−2i2i−2i2i002i−2i-2200002-22i2i−2i−2i22-2-20000000000000000-22−2i2i−i2i2i2−i2−222−2−222−2−i2i2i2−i22−2−22i2−i2−i2i2−i2i2i2−i2−222−20000000000000000
χ7122-2-22i2i−2i−2i00-22−2i2i−2i2i002i−2i-2200002-2−2i−2i2i2i-2-22200000000000000002-22i−2ii2−i2−i2i22−2−222−2−22i2−i2−i2i22−2−22i2−i2−i2i2−i2i2i2−i2−222−20000000000000000
χ7222-2-22i2i−2i−2i00-22−2i2i−2i2i002i−2i-2200002-2−2i−2i2i2i-2-22200000000000000002-22i−2i−i2i2i2−i2−222−2−222−2−i2i2i2−i2−222−2−i2i2i2−i2i2−i2−i2i22−2−220000000000000000
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χ7422-2-2−2i−2i2i2i002-22i−2i−2i2i002i−2i-220000-222i2i−2i−2i-2-2220000000000000000-222i−2i−222−2−i2i2i2−i2i2−i2−i2i22−2−22−i2i2i2−i2−222−2−222−2−i2i2i2−i20000000000000000
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χ8022-2-2−2i−2i2i2i002-2−2i2i−2i2i00−2i2i2-200002-200000000-2-2222i2i−2i−2i00002i−2i-220000−i2i2−i2i22−22−22−22−2−i2i2−i2i2−22−22i2−i2i2−i2i2−i2i2−i2−22−220000000000000000
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χ904-44-44-44-44-40000000000004-40000−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000000000000000000000000000
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χ924-44-44-44-4-44000000000000-440000−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ934-44-4-44-444-4000000000000-4400002i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000000000000000000000000000
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χ954-44-4-44-44-440000000000004-400002i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000000000000000000000000000
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χ994-4-444i−4i−4i4i00000000−4i4i000000-440022−22−2222−2i22i22i2−2i2−2i22i22i2−2i222−22−2222000000000000000000000000000000000000000000000000000000000000
χ1004-4-444i−4i−4i4i00000000−4i4i000000-4400−222222−222i2−2i2−2i22i22i2−2i2−2i22i2−222222−22000000000000000000000000000000000000000000000000000000000000
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χ1024-4-44−4i4i4i−4i000000004i−4i000000-4400−222222−22−2i22i22i2−2i2−2i22i22i2−2i2−222222−22000000000000000000000000000000000000000000000000000000000000
χ1034-4-44−4i4i4i−4i00000000−4i4i0000004-40022−22−22222i2−2i2−2i22i2−2i22i22i2−2i2−222222−22000000000000000000000000000000000000000000000000000000000000
χ1044-4-44−4i4i4i−4i00000000−4i4i0000004-400−222222−22−2i22i22i2−2i22i2−2i2−2i22i222−22−2222000000000000000000000000000000000000000000000000000000000000

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