Finite Group Databasebeta

← Group #72343756

Character table — Group #72343756

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size111111112222222222222222222244444444444444444444888888888888888888888888888888881616161616161616161616161616161616161616161616163232323232323232
order1222222244444444444488888888222244444444888888882444448888888888161616161616161616161616161616168888888888888888161616161616161688888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-111-1-1-1-1-1-111111111-111-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111111111111-1-111-1-1-1-1-1-111111111-111-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111111111-1-111-1-1-1-1-1-111111111-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-111
χ8111111111111111111111111111111-1-111-1-1-1-1-1-111111111-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1
χ91111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ101111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ121111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111
χ131111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1
χ141111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111
χ151111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ161111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1
χ17111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-11-11-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1i−ii−ii−ii−i
χ18111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-11-11-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−ii−ii−ii−ii
χ19111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-11-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii-1-111-1-111i−ii−i−ii−ii
χ20111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-11-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i-1-111-1-111−ii−iii−ii−i
χ21111111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-111-1-1-1-111111-1-1-11-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii-1-111-1-111i−i−iii−i−ii
χ22111111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-111-1-1-1-111111-1-1-11-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i-1-111-1-111−iii−i−iii−i
χ23111111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-111-1-1-1-111111-1-1-11-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i11-1-111-1-1i−i−ii−iii−i
χ24111111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-111-1-1-1-111111-1-1-11-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii11-1-111-1-1−iii−ii−i−ii
χ25111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−iii−i−iii−i−i−i−iii11-1-1-1-111−ii−ii−iii−i
χ26111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iii−i−iii−i−iiiii−i−i11-1-1-1-111i−ii−ii−i−ii
χ27111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1ii−i−iii−i−i−i−iiiii−i−i-1-11111-1-1−ii−iii−i−ii
χ28111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1−i−iii−i−iiiii−i−i−i−iii-1-11111-1-1i−ii−i−iii−i
χ29111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-11111-1-11111-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−iii−i−i-1-11111-1-1−iii−i−ii−ii
χ30111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-11111-1-11111-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iii−i−iii-1-11111-1-1i−i−iii−ii−i
χ31111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iii−i−iii11-1-1-1-111−iii−ii−ii−i
χ32111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−iii−i−i11-1-1-1-111i−i−ii−ii−ii
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χ3422222222222222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ3522222222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-22222-2-2-222-222-2-2-2-22222000000000000000000000000000000000000000000000000
χ3622222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222-2-2-2-22222222-2-2-2-2000000000000000000000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222-2-22222-2-2-2-2-2-2-22-2222-2-222-2-222000000000000000000000000000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2222222-2-2-2-22-2-2-22-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ39222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-222222222222222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ40222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222222222-222-222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ4122222222-2-2-2-22222-2-2-2-2000000002222-2-22222-2-20000000022-2-2-2-20000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ4222222222-2-2-2-22222-2-2-2-2000000002222-2-22222-2-20000000022-2-2-2-20000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ4322222222-2-2-2-22222-2-2-2-20000000022-2-2-2-2-2-2-2-22200000000-22-22220000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ4422222222-2-2-2-22222-2-2-2-20000000022-2-2-2-2-2-2-2-22200000000-22-22220000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ4522222222-2-2-2-22222-2-2-2-200000000-2-2222222-2-22200000000-2-22-2-220000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ4622222222-2-2-2-22222-2-2-2-200000000-2-2222222-2-22200000000-2-22-2-220000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ4722222222-2-2-2-22222-2-2-2-200000000-2-2-2-222-2-222-2-2000000002-2222-20000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ4822222222-2-2-2-22222-2-2-2-200000000-2-2-2-222-2-222-2-2000000002-2222-20000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ4922222222-2-2-2-2-2-2-2-22222000000002222-2-2-2-2222200000000-2-22-22-20000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ5022222222-2-2-2-2-2-2-2-22222000000002222-2-2-2-2222200000000-2-22-22-20000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ5122222222-2-2-2-2-2-2-2-222220000000022-2-2-2-222-2-2-2-2000000002-222-220000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ5222222222-2-2-2-2-2-2-2-222220000000022-2-2-2-222-2-2-2-2000000002-222-220000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ5322222222-2-2-2-2-2-2-2-2222200000000-2-22222-2-2-2-2-2-20000000022-2-2220000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ5422222222-2-2-2-2-2-2-2-2222200000000-2-22222-2-2-2-2-2-20000000022-2-2220000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ5522222222-2-2-2-2-2-2-2-2222200000000-2-2-2-22222222200000000-22-22-2-20000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ5622222222-2-2-2-2-2-2-2-2222200000000-2-2-2-22222222200000000-22-22-2-20000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000i2−i2−i2i2−i2i2i2−i200000000
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χ8044-44-4-44-40000000000002i2−2i22i2−2i22i2−2i22i2−2i200004i−4i-4400−4i4i00002222−22−220000000000−2i22i200−2222000000000000000000000000000000000000000000000000
χ8144-44-4-44-40000000000002i2−2i22i2−2i22i2−2i22i2−2i20000−4i4i4-400−4i4i0000−22−22222200000000002i2−2i200−2222000000000000000000000000000000000000000000000000
χ8244-44-4-44-40000000000002i2−2i22i2−2i22i2−2i22i2−2i20000−4i4i-44004i−4i0000−22−2222220000000000−2i22i20022−22000000000000000000000000000000000000000000000000
χ8344-44-4-44-4000000000000−2i22i2−2i22i2−2i22i2−2i22i200004i−4i4-4004i−4i0000−22−2222220000000000−2i22i200−2222000000000000000000000000000000000000000000000000
χ8444-44-4-44-4000000000000−2i22i2−2i22i2−2i22i2−2i22i200004i−4i-4400−4i4i0000−22−22222200000000002i2−2i20022−22000000000000000000000000000000000000000000000000
χ8544-44-4-44-4000000000000−2i22i2−2i22i2−2i22i2−2i22i20000−4i4i4-400−4i4i00002222−22−220000000000−2i22i20022−22000000000000000000000000000000000000000000000000
χ8644-44-4-44-4000000000000−2i22i2−2i22i2−2i22i2−2i22i20000−4i4i-44004i−4i00002222−22−2200000000002i2−2i200−2222000000000000000000000000000000000000000000000000
χ874-44-44-44-40000000000002i2−2i2−2i22i2−2i22i22i2−2i24-44-400004-40000002i2−2i22i2−2i2000000002i2−2i2002i2−2i200000000000000000000000000000000000000000000000000
χ884-44-44-44-40000000000002i2−2i2−2i22i2−2i22i22i2−2i24-4-440000-440000002i2−2i22i2−2i200000000−2i22i200−2i22i200000000000000000000000000000000000000000000000000
χ894-44-44-44-40000000000002i2−2i2−2i22i2−2i22i22i2−2i2-444-40000-44000000−2i22i2−2i22i2000000002i2−2i200−2i22i200000000000000000000000000000000000000000000000000
χ904-44-44-44-40000000000002i2−2i2−2i22i2−2i22i22i2−2i2-44-4400004-4000000−2i22i2−2i22i200000000−2i22i2002i2−2i200000000000000000000000000000000000000000000000000
χ914-44-44-44-4000000000000−2i22i22i2−2i22i2−2i2−2i22i24-44-400004-4000000−2i22i2−2i22i200000000−2i22i200−2i22i200000000000000000000000000000000000000000000000000
χ924-44-44-44-4000000000000−2i22i22i2−2i22i2−2i2−2i22i24-4-440000-44000000−2i22i2−2i22i2000000002i2−2i2002i2−2i200000000000000000000000000000000000000000000000000
χ934-44-44-44-4000000000000−2i22i22i2−2i22i2−2i2−2i22i2-444-40000-440000002i2−2i22i2−2i200000000−2i22i2002i2−2i200000000000000000000000000000000000000000000000000
χ944-44-44-44-4000000000000−2i22i22i2−2i22i2−2i2−2i22i2-44-4400004-40000002i2−2i22i2−2i2000000002i2−2i200−2i22i200000000000000000000000000000000000000000000000000
χ954-4-4444-4-44-4-444i−4i4i−4i−4i4i−4i4i0000000000000000000000000000000000000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000000000
χ964-4-4444-4-44-4-444i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000000000
χ974-4-4444-4-44-4-44−4i4i−4i4i4i−4i4i−4i0000000000000000000000000000000000000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000000000
χ984-4-4444-4-44-4-44−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000000000
χ994-4-4444-4-4-444-44i−4i4i−4i4i−4i4i−4i-4-444-4-444000000000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ1004-4-4444-4-4-444-4−4i4i−4i4i−4i4i−4i4i-4-444-4-4440000000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-4-4-444444-4-44-4-44-444-40000000000000000000000004i−4i−4i4i0000004i−4i00000000000000000000000000000000000000000000000000000000
χ1024-4-4-4-444444-4-44-4-44-444-4000000000000000000000000−4i4i4i−4i000000−4i4i00000000000000000000000000000000000000000000000000000000
χ1034-4-4-4-444444-4-4-444-44-4-440000000000000000000000004i−4i−4i4i000000−4i4i00000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-444444-4-4-444-44-4-44000000000000000000000000−4i4i4i−4i0000004i−4i00000000000000000000000000000000000000000000000000000000
χ1054-4-4-4-4444-4-4444-4-444-4-4444-4-4-4-4440000000000004-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ1064-4-4-4-4444-4-4444-4-444-4-44-4-44444-4-4000000000000-444-400000000000000000000000000000000000000000000000000000000000000000000
χ1074-4-4-4-4444-4-444-444-4-444-444-4-4-4-444000000000000-444-400000000000000000000000000000000000000000000000000000000000000000000
χ1084-4-4-4-4444-4-444-444-4-444-4-4-44444-4-40000000000004-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-88-8-880000000000004i2−4i24i2−4i2−4i24i2−4i24i2000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11088-8-88-8-88000000000000−4i24i2−4i24i24i2−4i24i2−4i2000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-888-8-8-880000000000004i2−4i2−4i24i24i2−4i2−4i24i2000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-888-8-8-88000000000000−4i24i24i2−4i2−4i24i24i2−4i2000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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