Finite Group Databasebeta

← Group #110256

Character table — Group #110256

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222222222222244444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222444444442222444444444444444444444444444444444444888888888888888888888888888888884444444488888888
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
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ171-1-11-1-11111-1-111-1-111-1-111-1-11111-1-111-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1i−ii−i1-11-11-11-1i−ii−i
χ181-1-11-1-11111-1-111-1-111-1-111-1-11111-1-111-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1−ii−ii-11-11-11-11−ii−ii
χ191-1-11-1-11111-1-111-1-111-1-111-1-11111-1-111-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111i−ii−i-11-111-11-1−ii−ii
χ201-1-11-1-11111-1-111-1-111-1-111-1-11111-1-111-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111−ii−ii1-11-1-11-11i−ii−i
χ211-1-11-1-11111-1-111-1-111-1-111-1-11111-1-111-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111i−ii−i1-11-1-11-11−ii−ii
χ221-1-11-1-11111-1-111-1-111-1-111-1-11111-1-111-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−ii−ii-11-111-11-1i−ii−i
χ231-1-11-1-11111-1-111-1-111-1-111-1-11111-1-111-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1i−ii−i-11-11-11-11i−ii−i
χ241-1-11-1-11111-1-111-1-111-1-111-1-11111-1-111-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−ii−ii1-11-11-11-1−ii−ii
χ251-1-11-1-111-1-111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−ii−i−ii1-1-11−iii−i1-1-11
χ261-1-11-1-111-1-111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−iii−i-111-1i−i−ii-111-1
χ271-1-11-1-111-1-111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiii−i−ii-111-1−iii−i-111-1
χ281-1-11-1-111-1-111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−iii−i1-1-11i−i−ii1-1-11
χ291-1-11-1-111-1-111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiii−i−ii1-1-11i−i−ii-111-1
χ301-1-11-1-111-1-111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−iii−i-111-1−iii−i1-1-11
χ311-1-11-1-111-1-111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−ii−i−ii-111-1i−i−ii1-1-11
χ321-1-11-1-111-1-111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−iii−i1-1-11−iii−i-111-1
χ33222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-2-2-2220000000000000000000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ362222222222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-2-2-22200000000000000000000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ372222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-22222-2-2000000000000000022-2-222-2-222-2-222-2-200000000000000000000000000000000
χ382222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-22222-2-20000000000000000-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-22222-2-222-2-2-2-2000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-22222-2-222-2-2-2-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ4122222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-2-2-222-2-22222000000000000000022-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-2-2-222-2-222220000000000000000-2-222-2-22222-2-222-2-200000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222222-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222222-2-222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ452222-2-2-2-22222-2-2-2-22-22-22-22-20000000000000000002-2002-2002-2002-22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−20000000000000000
χ462222-2-2-2-22222-2-2-2-22-22-22-22-20000000000000000002-2002-2002-2002-2−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−220000000000000000
χ472222-2-2-2-22222-2-2-2-22-22-22-22-2000000000000000000-2200-2200-2200-222−22−22−22−22−22−22−22−2−22−22−22−22−22−22−22−220000000000000000
χ482222-2-2-2-22222-2-2-2-22-22-22-22-2000000000000000000-2200-2200-2200-22−22−22−22−22−22−22−22−222−22−22−22−22−22−22−22−20000000000000000
χ492222-2-2-2-22222-2-2-2-2-22-22-22-2200000000000000002-2002-2002-2002-2002−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−220000000000000000
χ502222-2-2-2-22222-2-2-2-2-22-22-22-2200000000000000002-2002-2002-2002-200−222−2−222−2−222−2−222−2−222−2−222−2−222−2−222−20000000000000000
χ512222-2-2-2-22222-2-2-2-2-22-22-22-220000000000000000-2200-2200-2200-22002−2−222−2−222−2−222−2−22−222−2−222−2−222−2−222−20000000000000000
χ522222-2-2-2-22222-2-2-2-2-22-22-22-220000000000000000-2200-2200-2200-2200−222−2−222−2−222−2−222−22−2−222−2−222−2−222−2−220000000000000000
χ532222-2-2-2-2-2-2-2-222222-22-2-22-2200000000000000002i−2i002i−2i00−2i2i00−2i2i002−2−222−2−22−222−2−222−2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ542222-2-2-2-2-2-2-2-222222-22-2-22-2200000000000000002i−2i002i−2i00−2i2i00−2i2i00−222−2−222−22−2−222−2−22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ552222-2-2-2-2-2-2-2-222222-22-2-22-220000000000000000−2i2i00−2i2i002i−2i002i−2i002−2−222−2−22−222−2−222−2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
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χ572222-2-2-2-2-2-2-2-22222-22-222-22-20000000000000000002i−2i002i−2i00−2i2i00−2i2i2−22−22−22−2−22−22−22−22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
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χ622-2-2222-2-222-2-2-2-2222-2-222-2-220000000000000000002i−2i00−2i2i002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−22−222−22−2−22−222−22−20000000000000000
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χ692-2-2222-2-2-2-22222-2-22-2-22-222-200000000000000002-200-2200-22002-200i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ702-2-2222-2-2-2-22222-2-22-2-22-222-200000000000000002-200-2200-22002-200−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ712-2-2222-2-2-2-22222-2-22-2-22-222-20000000000000000-22002-2002-200-2200i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ722-2-2222-2-2-2-22222-2-22-2-22-222-20000000000000000-22002-2002-200-2200−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ732-2-2222-2-2-2-22222-2-2-222-22-2-220000000000000000002-200-2200-22002-2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
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χ752-2-2222-2-2-2-22222-2-2-222-22-2-22000000000000000000-22002-2002-200-22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
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χ772-2-22-2-22222-2-222-2-222-2-222-2-2-2-2-2-222-2-2222222-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ782-2-22-2-22222-2-222-2-222-2-222-2-2-2-2-2-222-2-2222222-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ792-2-22-2-22222-2-222-2-2-2-222-2-22222-2-2-2-2-2-2-2-22222220000000000000000000000000000000022-2-2-2-22222-2-2-2-2220000000000000000
χ802-2-22-2-22222-2-222-2-2-2-222-2-22222-2-2-2-2-2-2-2-222222200000000000000000000000000000000-2-22222-2-2-2-22222-2-20000000000000000
χ812-2-22-2-22222-2-222-2-2-2-222-2-222-2-222222222-2-2-2-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ822-2-22-2-22222-2-222-2-2-2-222-2-222-2-222222222-2-2-2-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ832-2-22-2-222-2-222-2-22222-2-2-2-22222-2-2-2-22222-2-222-2-2000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ842-2-22-2-222-2-222-2-22222-2-2-2-22222-2-2-2-22222-2-222-2-200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ852-2-22-2-222-2-222-2-22222-2-2-2-222-2-22222-2-2-2-222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ862-2-22-2-222-2-222-2-22222-2-2-2-222-2-22222-2-2-2-222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ872-2-22-2-222-2-222-2-222-2-22222-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ882-2-22-2-222-2-222-2-222-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ8944-4-44-44-44i−4i4i−4i4i−4i4i−4i00000000004-4004i−4i004i−4i4-4000000000000000000000000000000000000000000000000000000000000000000
χ9044-4-44-44-44i−4i4i−4i4i−4i4i−4i0000000000-4400−4i4i00−4i4i-44000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-44-44-4−4i4i−4i4i−4i4i−4i4i00000000004-400−4i4i00−4i4i4-4000000000000000000000000000000000000000000000000000000000000000000
χ9244-4-44-44-4−4i4i−4i4i−4i4i−4i4i0000000000-44004i−4i004i−4i-44000000000000000000000000000000000000000000000000000000000000000000
χ9344-4-4-44-444i−4i4i−4i−4i4i−4i4i000000004-4004-4004i−4i00004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ9444-4-4-44-444i−4i4i−4i−4i4i−4i4i00000000-4400-4400−4i4i0000−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ9544-4-4-44-44−4i4i−4i4i4i−4i4i−4i000000004-4004-400−4i4i0000−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ9644-4-4-44-44−4i4i−4i4i4i−4i4i−4i00000000-4400-44004i−4i00004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ974-44-44-4-444i−4i−4i4i−4i4i4i−4i000000004-400-4400−4i4i00004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ984-44-44-4-444i−4i−4i4i−4i4i4i−4i00000000-44004-4004i−4i0000−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ994-44-44-4-44−4i4i4i−4i4i−4i−4i4i000000004-400-44004i−4i0000−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ1004-44-44-4-44−4i4i4i−4i4i−4i−4i4i00000000-44004-400−4i4i00004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ1014-44-4-444-44i−4i−4i4i4i−4i−4i4i00000000004-4004i−4i00−4i4i-44000000000000000000000000000000000000000000000000000000000000000000
χ1024-44-4-444-44i−4i−4i4i4i−4i−4i4i0000000000-4400−4i4i004i−4i4-4000000000000000000000000000000000000000000000000000000000000000000
χ1034-44-4-444-4−4i4i4i−4i−4i4i4i−4i00000000004-400−4i4i004i−4i-44000000000000000000000000000000000000000000000000000000000000000000
χ1044-44-4-444-4−4i4i4i−4i−4i4i4i−4i0000000000-44004i−4i00−4i4i4-4000000000000000000000000000000000000000000000000000000000000000000

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