Finite Group Databasebeta

← Group #380607

Character table — Group #380607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222222222222244444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222222224444444444444444444444444444444444444444888888888888888888888888888888882222444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-111
χ91111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1
χ121111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ171-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−ii−ii−i1-11-1
χ181-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii−ii−ii-11-11
χ191-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii−ii−ii1-11-1
χ201-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−ii−ii−i-11-11
χ211-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-11i−ii−i−ii−ii1-1-11
χ221-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-111-1−ii−iii−ii−i-111-1
χ231-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-1-11−ii−iii−ii−i1-1-11
χ241-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-111-1i−ii−i−ii−ii-111-1
χ251-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-11-1i−i−iii−i−ii-11-11
χ261-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-11-11−iii−i−iii−i1-11-1
χ271-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-1−iii−i−iii−i-11-11
χ281-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-11i−i−iii−i−ii1-11-1
χ291-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-1-11i−i−ii−iii−i-111-1
χ301-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1−iii−ii−i−ii1-1-11
χ311-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-11−iii−ii−i−ii-111-1
χ321-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1i−i−ii−iii−i1-1-11
χ3322222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ3422222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-222-2-222-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ372222222-2-2-2-2-2-2-2-2222-2-222-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ382222222-2-2-2-2-2-2-2-2222-2-222-2-222-2-222-2-222-2-222-2-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ392222222-2-2-2-2-2-2-2-2222-2-2-2-22222-2-2-2-222-2-222-2-22200000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ402222222-2-2-2-2-2-2-2-2222-2-2-2-22222-2-2-2-222-2-222-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ412222222-2-2-2-2-2-2-2-22-2-22222-2-2-2-22222-2-2-2-222-2-22200000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ422222222-2-2-2-2-2-2-2-22-2-22222-2-2-2-22222-2-2-2-222-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ432222222-2-2-2-2-2-2-2-22-2-222-2-222-2-222-2-22222-2-222-2-2000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ442222222-2-2-2-2-2-2-2-22-2-222-2-222-2-222-2-22222-2-222-2-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
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χ46222-2-22-222-2-222-2-2-200002i−2i2i−2i00002i−2i2i−2i00000000002-2002-22i−2i002i−2i00−i2i2−i2i2−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
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χ50222-2-22-222-2-222-2-2-20000−2i2i−2i2i0000−2i2i−2i2i00000000002-2002-2−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ51222-2-22-222-2-222-2-2-20000−2i2i−2i2i0000−2i2i−2i2i0000000000-2200-222i−2i002i−2i00i2−i2i2−i2i2−i2i2−i2−22−22−22−22−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ52222-2-22-222-2-222-2-2-20000−2i2i−2i2i0000−2i2i−2i2i0000000000-2200-222i−2i002i−2i00−i2i2−i2i2−i2i2−i2i22−22−22−22−2i2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ53222-2-22-2-2-222-2-222-200002i−2i−2i2i00002i−2i−2i2i000000002-2002-200002i−2i002i−2i2−2−222−2−22i2−i2−i2i2i2−i2−i2i22−2−222−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ54222-2-22-2-2-222-2-222-200002i−2i−2i2i00002i−2i−2i2i000000002-2002-200002i−2i002i−2i−222−2−222−2−i2i2i2−i2−i2i2i2−i2−222−2−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
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χ652-2-2222-222-2-2-2-222-20000−2i2i−2i2i00002i−2i2i−2i00000000002-200-22−2i2i002i−2i002−22−2−22−22i2−i2i2−i2−i2i2−i2i22−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
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χ672-2-2222-222-2-2-2-222-20000−2i2i−2i2i00002i−2i2i−2i0000000000-22002-22i−2i00−2i2i002−22−2−22−22i2−i2i2−i2−i2i2−i2i2−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
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χ732-2-2222-2-2-22222-2-2-20000−2i2i2i−2i00002i−2i−2i2i000000002-200-220000−2i2i002i−2ii2−i2−i2i2−i2i2i2−i22−2−22−222−2i2−i2−i2i2−i2i2i2−i2−222−22−2−220000000000000000
χ742-2-2222-2-2-22222-2-2-20000−2i2i2i−2i00002i−2i−2i2i000000002-200-220000−2i2i002i−2i−i2i2i2−i2i2−i2−i2i2−222−22−2−22−i2i2i2−i2i2−i2−i2i22−2−22−222−20000000000000000
χ752-2-2222-2-2-22222-2-2-20000−2i2i2i−2i00002i−2i−2i2i00000000-22002-200002i−2i00−2i2ii2−i2−i2i2−i2i2i2−i22−2−22−222−2−i2i2i2−i2i2−i2−i2i22−2−22−222−20000000000000000
χ762-2-2222-2-2-22222-2-2-20000−2i2i2i−2i00002i−2i−2i2i00000000-22002-200002i−2i00−2i2i−i2i2i2−i2i2−i2−i2i2−222−22−2−22i2−i2−i2i2−i2i2i2−i2−222−22−2−220000000000000000
χ772-2-2-2-2222222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000000
χ782-2-2-2-2222222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ792-2-2-2-2222222-2-2-2-22-2-2-2-222222222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ802-2-2-2-2222222-2-2-2-22-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ812-2-2-2-222-2-2-2-22222222-2-222-2-2-2-222-2-22222-2-2-2-2220000000000000000000000000000000022-2-2-2-22222-2-2-2-2220000000000000000
χ822-2-2-2-222-2-2-2-22222222-2-222-2-2-2-222-2-22222-2-2-2-22200000000000000000000000000000000-2-22222-2-2-2-22222-2-20000000000000000
χ832-2-2-2-222-2-2-2-22222222-2-2-2-222-2-22222-2-2-2-22222-2-2000000000000000022-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ842-2-2-2-222-2-2-2-22222222-2-2-2-222-2-22222-2-2-2-22222-2-20000000000000000-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ852-2-2-2-222-2-2-2-222222-2-22222-2-222-2-2-2-222-2-22222-2-2000000000000000022-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ862-2-2-2-222-2-2-2-222222-2-22222-2-222-2-2-2-222-2-22222-2-20000000000000000-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ872-2-2-2-222-2-2-2-222222-2-222-2-22222-2-222-2-222-2-2-2-2220000000000000000000000000000000022-2-2-2-222-2-22222-2-20000000000000000
χ882-2-2-2-222-2-2-2-222222-2-222-2-22222-2-222-2-222-2-2-2-22200000000000000000000000000000000-2-22222-2-222-2-2-2-2220000000000000000
χ8944-44-4-444-44-44-44-4-44i−4i4i−4i00004i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ9044-44-4-444-44-44-44-4-4−4i4i−4i4i0000−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-44-4-44-44-44-44-44-44i−4i−4i4i00004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ9244-44-4-44-44-44-44-44-4−4i4i4i−4i0000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ9344-4-44-4-44-4-444-4-44400000000000000004-44-44-44-40000000000000000000000000000000000000000000000000000000000000000
χ9444-4-44-4-44-4-444-4-4440000000000000000-44-44-44-440000000000000000000000000000000000000000000000000000000000000000
χ9544-4-44-4-4-444-4-444-4400000000000000004-4-444-4-440000000000000000000000000000000000000000000000000000000000000000
χ9644-4-44-4-4-444-4-444-440000000000000000-444-4-444-40000000000000000000000000000000000000000000000000000000000000000
χ974-444-4-4-44-4-44-444-4400000000000000004-44-4-44-440000000000000000000000000000000000000000000000000000000000000000
χ984-444-4-4-44-4-44-444-440000000000000000-44-444-44-40000000000000000000000000000000000000000000000000000000000000000
χ994-444-4-4-4-444-44-4-44400000000000000004-4-44-444-40000000000000000000000000000000000000000000000000000000000000000
χ1004-444-4-4-4-444-44-4-4440000000000000000-444-44-4-440000000000000000000000000000000000000000000000000000000000000000
χ1014-44-44-444-44-4-44-44-44i−4i4i−4i0000−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-44-44-444-44-4-44-44-4−4i4i−4i4i00004i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-44-44-44-44-444-44-4-44i−4i−4i4i0000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-44-44-44-44-444-44-4-4−4i4i4i−4i00004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000000

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