Finite Group Databasebeta

← Group #225614

Character table — Group #225614

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888822444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ121111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ171111-1-1-1-1-1-1-11111-11111-1-1-1-11111-1-1-1-1-111-1-111-1-1ii−i−iii−i−i111-1-111-1-11111-1-1-1-11-11-1i−ii−i11-1-111-1-1ii−i−iii−i−ii−ii−ii−ii−i
χ181111-1-1-1-1-1-1-11111-11111-1-1-1-11111-1-1-1-1-111-1-111-1-1−i−iii−i−iii111-1-111-1-11111-1-1-1-11-11-1−ii−ii11-1-111-1-1−i−iii−i−iii−ii−ii−ii−ii
χ191111-1-1-1-1-1-1-11111-11111-1-1-1-11111-1-1-1-1-1-1-111-1-111ii−i−iii−i−i111-1-111-1-11111-1-1-1-1-11-11i−ii−i-1-111-1-111ii−i−iii−i−i−ii−ii−ii−ii
χ201111-1-1-1-1-1-1-11111-11111-1-1-1-11111-1-1-1-1-1-1-111-1-111−i−iii−i−iii111-1-111-1-11111-1-1-1-1-11-11−ii−ii-1-111-1-111−i−iii−i−iiii−ii−ii−ii−i
χ211111-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11111-111-1-111-1-1ii−i−i−i−iii111-1-1-1-111-1-1-1-111111-11-1i−i−ii-1-111-1-111ii−i−i−i−iiii−i−iii−i−ii
χ221111-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11111-111-1-111-1-1−i−iiiii−i−i111-1-1-1-111-1-1-1-111111-11-1−iii−i-1-111-1-111−i−iiiii−i−i−iii−i−iii−i
χ231111-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11111-1-1-111-1-111ii−i−i−i−iii111-1-1-1-111-1-1-1-11111-11-11i−i−ii11-1-111-1-1ii−i−i−i−iii−iii−i−iii−i
χ241111-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11111-1-1-111-1-111−i−iiiii−i−i111-1-1-1-111-1-1-1-11111-11-11−iii−i11-1-111-1-1−i−iiiii−i−ii−i−iii−i−ii
χ251111-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-111-1-1-1-111ii−i−iii−i−i1-1-11111-1-1-1-1-1-111111-1-11i−ii−i11-1-1-1-111−i−iii−i−iiii−ii−i−ii−ii
χ261111-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-111-1-1-1-111−i−iii−i−iii1-1-11111-1-1-1-1-1-111111-1-11−ii−ii11-1-1-1-111ii−i−iii−i−i−ii−iii−ii−i
χ271111-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1ii−i−iii−i−i1-1-11111-1-1-1-1-1-11111-111-1i−ii−i-1-11111-1-1−i−iii−i−iii−ii−iii−ii−i
χ281111-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1−i−iii−i−iii1-1-11111-1-1-1-1-1-11111-111-1−ii−ii-1-11111-1-1ii−i−iii−i−ii−ii−i−ii−ii
χ291111-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-111-1-1-1-111ii−i−i−i−iii1-1-111-1-1111111-1-1-1-11-1-11i−i−ii-1-11111-1-1−i−iiiii−i−ii−i−ii−iii−i
χ301111-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-111-1-1-1-111−i−iiiii−i−i1-1-111-1-1111111-1-1-1-11-1-11−iii−i-1-11111-1-1ii−i−i−i−iii−iii−ii−i−ii
χ311111-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-1-1-11111-1-1ii−i−i−i−iii1-1-111-1-1111111-1-1-1-1-111-1i−i−ii11-1-1-1-111−i−iiiii−i−i−iii−ii−i−ii
χ321111-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-1-1-11111-1-1−i−iiiii−i−i1-1-111-1-1111111-1-1-1-1-111-1−iii−i11-1-1-1-111ii−i−i−i−iiii−i−ii−iii−i
χ332222222222-2-2-222-20000000022222222-20000000022222222-20000-2-2-2-2000000000000-2-2-2-2000000000000000000000000
χ342222222222-2-2-222-20000000022222222-200000000-2-2-2-2-2-2-2-2-20000-2-2-2-20000000000002222000000000000000000000000
χ352222222222-2-2-222-200000000-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2-200002222000000000000-2-222000000000000000000000000
χ362222222222-2-2-222-200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-22222-20000222200000000000022-2-2000000000000000000000000
χ3722222222-2-2222-2-222222222200000000-22222222200000000-2-2-2-2-2000000000000-2-2-2-20000000000000000000000000000
χ3822222222-2-2222-2-222222222200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-2-200000000000022220000000000000000000000000000
χ3922222222-2-2222-2-22-2-2-2-2-2-2-2-200000000-22222-2-2-2-200000000-22222000000000000-2-2220000000000000000000000000000
χ4022222222-2-2222-2-22-2-2-2-2-2-2-2-200000000-2-2-2-2-2222200000000-2222200000000000022-2-20000000000000000000000000000
χ412222-2-2-2-222-222-2-2-22222-2-2-2-200000000222-2-222-2-200000000-2-2-222000000000000-22-220000000000000000000000000000
χ422222-2-2-2-222-222-2-2-22222-2-2-2-2000000002-2-222-2-22200000000-2-2-2220000000000002-22-20000000000000000000000000000
χ432222-2-2-2-222-222-2-2-2-2-2-2-2222200000000222-2-2-2-22200000000-222-2-2000000000000-222-20000000000000000000000000000
χ442222-2-2-2-222-222-2-2-2-2-2-2-22222000000002-2-22222-2-200000000-222-2-20000000000002-2-220000000000000000000000000000
χ452222-2-2-2-2-2-22-2-2222000000002222-2-2-2-22000000002i2i−2i−2i2i2i−2i−2i-20000-2-222000000000000−2i2i−2i2i000000000000000000000000
χ462222-2-2-2-2-2-22-2-2222000000002222-2-2-2-2200000000−2i−2i2i2i−2i−2i2i2i-20000-2-2220000000000002i−2i2i−2i000000000000000000000000
χ472222-2-2-2-2-2-22-2-222200000000-2-2-2-222222000000002i2i−2i−2i−2i−2i2i2i-2000022-2-2000000000000−2i2i2i−2i000000000000000000000000
χ482222-2-2-2-2-2-22-2-222200000000-2-2-2-22222200000000−2i−2i2i2i2i2i−2i−2i-2000022-2-20000000000002i−2i−2i2i000000000000000000000000
χ4922-2-222-2-200-22-20022i2i−2i−2i2i2i−2i−2i22−2−222−2−202i−2i2i−2i2-22-200000000000002−22−2i2i2−i2−i2i2i2−i2−i200000000i2−i2i2−i22−22−20000000000000000
χ5022-2-222-2-200-22-20022i2i−2i−2i2i2i−2i−2i22−2−222−2−20−2i2i−2i2i-22-2200000000000002−22−2i2i2−i2−i2i2i2−i2−i200000000−i2i2−i2i2−22−220000000000000000
χ5122-2-222-2-200-22-20022i2i−2i−2i2i2i−2i−2i−2−222−2−22202i−2i2i−2i2-22-20000000000000−22−22−i2−i2i2i2−i2−i2i2i200000000−i2i2−i2i2−22−220000000000000000
χ5222-2-222-2-200-22-20022i2i−2i−2i2i2i−2i−2i−2−222−2−2220−2i2i−2i2i-22-220000000000000−22−22−i2−i2i2i2−i2−i2i2i200000000i2−i2i2−i22−22−20000000000000000
χ5322-2-222-2-200-22-2002−2i−2i2i2i−2i−2i2i2i22−2−222−2−202i−2i2i−2i-22-2200000000000002−22−2−i2−i2i2i2−i2−i2i2i200000000i2−i2i2−i2−22−220000000000000000
χ5422-2-222-2-200-22-2002−2i−2i2i2i−2i−2i2i2i22−2−222−2−20−2i2i−2i2i2-22-200000000000002−22−2−i2−i2i2i2−i2−i2i2i200000000−i2i2−i2i22−22−20000000000000000
χ5522-2-222-2-200-22-2002−2i−2i2i2i−2i−2i2i2i−2−222−2−22202i−2i2i−2i-22-220000000000000−22−22i2i2−i2−i2i2i2−i2−i200000000−i2i2−i2i22−22−20000000000000000
χ5622-2-222-2-200-22-2002−2i−2i2i2i−2i−2i2i2i−2−222−2−2220−2i2i−2i2i2-22-20000000000000−22−22i2i2−i2−i2i2i2−i2−i200000000i2−i2i2−i2−22−220000000000000000
χ5722-2-2-2-2220022-200-22i2i−2i−2i−2i−2i2i2i22−2−2−2−22202i−2i−2i2i2-2-2200000000000002−2−22i2i2−i2−i2−i2−i2i2i200000000i2−i2−i2i22−2−220000000000000000
χ5822-2-2-2-2220022-200-22i2i−2i−2i−2i−2i2i2i22−2−2−2−2220−2i2i2i−2i-222-200000000000002−2−22i2i2−i2−i2−i2−i2i2i200000000−i2i2i2−i2−222−20000000000000000
χ5922-2-2-2-2220022-200-22i2i−2i−2i−2i−2i2i2i−2−22222−2−202i−2i−2i2i2-2-220000000000000−222−2−i2−i2i2i2i2i2−i2−i200000000−i2i2i2−i2−222−20000000000000000
χ6022-2-2-2-2220022-200-22i2i−2i−2i−2i−2i2i2i−2−22222−2−20−2i2i2i−2i-222-20000000000000−222−2−i2−i2i2i2i2i2−i2−i200000000i2−i2−i2i22−2−220000000000000000
χ6122-2-2-2-2220022-200-2−2i−2i2i2i2i2i−2i−2i22−2−2−2−22202i−2i−2i2i-222-200000000000002−2−22−i2−i2i2i2i2i2−i2−i200000000i2−i2−i2i2−222−20000000000000000
χ6222-2-2-2-2220022-200-2−2i−2i2i2i2i2i−2i−2i22−2−2−2−2220−2i2i2i−2i2-2-2200000000000002−2−22−i2−i2i2i2i2i2−i2−i200000000−i2i2i2−i22−2−220000000000000000
χ6322-2-2-2-2220022-200-2−2i−2i2i2i2i2i−2i−2i−2−22222−2−202i−2i−2i2i-222-20000000000000−222−2i2i2−i2−i2−i2−i2i2i200000000−i2i2i2−i22−2−220000000000000000
χ6422-2-2-2-2220022-200-2−2i−2i2i2i2i2i−2i−2i−2−22222−2−20−2i2i2i−2i2-2-220000000000000−222−2i2i2−i2−i2−i2−i2i2i200000000i2−i2−i2i2−222−20000000000000000
χ652-22-22-22-22-20002-20i2−i2i2−i2i2−i2i2−i22i−2i2i−2i2i−2i2i−2i0000000002-22-22i−2i2i−2i0i2−i2i2−i200002−22−22−22−20000000000000000i2−i2i2−i22−22−200000000
χ662-22-22-22-22-20002-20i2−i2i2−i2i2−i2i2−i22i−2i2i−2i2i−2i2i−2i000000000-22-22−2i2i−2i2i0i2−i2i2−i200002−22−22−22−20000000000000000−i2i2−i2i2−22−2200000000
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χ692-22-22-22-22-20002-20−i2i2−i2i2−i2i2−i2i22i−2i2i−2i2i−2i2i−2i0000000002-22-22i−2i2i−2i0−i2i2−i2i20000−22−22−22−220000000000000000−i2i2−i2i2−22−2200000000
χ702-22-22-22-22-20002-20−i2i2−i2i2−i2i2−i2i22i−2i2i−2i2i−2i2i−2i000000000-22-22−2i2i−2i2i0−i2i2−i2i20000−22−22−22−220000000000000000i2−i2i2−i22−22−200000000
χ712-22-22-22-22-20002-20−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i−2i2i−2i2i0000000002-22-2−2i2i−2i2i0−i2i2−i2i200002−22−22−22−20000000000000000−i2i2−i2i22−22−200000000
χ722-22-22-22-22-20002-20−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i−2i2i−2i2i000000000-22-222i−2i2i−2i0−i2i2−i2i200002−22−22−22−20000000000000000i2−i2i2−i2−22−2200000000
χ732-22-2-22-22-220002-20i2−i2i2−i2−i2i2−i2i22i−2i2i−2i−2i2i−2i2i0000000002i−2i−2i2i-222-20i2−i2−i2i200002−22−2−22−220000000000000000−222−2i2−i2−i2i200000000
χ742-22-2-22-22-220002-20i2−i2i2−i2−i2i2−i2i22i−2i2i−2i−2i2i−2i2i000000000−2i2i2i−2i2-2-220i2−i2−i2i200002−22−2−22−2200000000000000002−2−22−i2i2i2−i200000000
χ752-22-2-22-22-220002-20i2−i2i2−i2−i2i2−i2i2−2i2i−2i2i2i−2i2i−2i0000000002i−2i−2i2i2-2-220i2−i2−i2i20000−22−222−22−20000000000000000−222−2−i2i2i2−i200000000
χ762-22-2-22-22-220002-20i2−i2i2−i2−i2i2−i2i2−2i2i−2i2i2i−2i2i−2i000000000−2i2i2i−2i-222-20i2−i2−i2i20000−22−222−22−200000000000000002−2−22i2−i2−i2i200000000
χ772-22-2-22-22-220002-20−i2i2−i2i2i2−i2i2−i22i−2i2i−2i−2i2i−2i2i0000000002i−2i−2i2i-222-20−i2i2i2−i20000−22−222−22−200000000000000002−2−22−i2i2i2−i200000000
χ782-22-2-22-22-220002-20−i2i2−i2i2i2−i2i2−i22i−2i2i−2i−2i2i−2i2i000000000−2i2i2i−2i2-2-220−i2i2i2−i20000−22−222−22−20000000000000000−222−2i2−i2−i2i200000000
χ792-22-2-22-22-220002-20−i2i2−i2i2i2−i2i2−i2−2i2i−2i2i2i−2i2i−2i0000000002i−2i−2i2i2-2-220−i2i2i2−i200002−22−2−22−2200000000000000002−2−22i2−i2−i2i200000000
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χ8144444444-4-4-4-4-4-4-4-40000000000000000400000000000000004000000000000000000000000000000000000000000000000
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χ8544-4-4-4-44400-4-44004000000002222−22−22−22−2222220000000000000000000000−222222−220000000000000000000000000000000000000000
χ8644-4-4-4-44400-4-4400400000000−22−2222222222−22−22000000000000000000000022−22−22220000000000000000000000000000000000000000
χ874-44-44-44-4-44000-4402i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ884-44-44-44-4-44000-440−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ894-44-4-44-444-4000-4402i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ904-44-4-44-444-4000-440−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ914-4-444-4-440000000022−22−222222−22−22222i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ924-4-444-4-440000000022−22−222222−22−2222−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ934-4-444-4-4400000000−222222−22−222222−222i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ944-4-444-4-4400000000−222222−22−222222−22−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ954-4-44-444-40000000022−22−2222−222222−222i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ964-4-44-444-40000000022−22−2222−222222−22−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ974-4-44-444-400000000−222222−2222−22−22222i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ984-4-44-444-400000000−222222−2222−22−2222−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000

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