Finite Group Databasebeta

← Group #229288

Character table — Group #229288

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888844444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ91111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ101111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-111-1-1
χ111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ121111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ171-11-11-11-1-11-1-1-1111iiii−i−i−i−i1111-1-1-1-1111-1-1ii−i−iii−i−iii−i−i-1ii−i−i11-1-1iiii−i−i−i−ii−ii−i1-1i−iii−i−i11-1-111-1-111-1-11-1i−i1-1i−i
χ181-11-11-11-1-11-1-1-1111iiii−i−i−i−i1111-1-1-1-1111-1-1ii−i−i−i−iii−i−iii-1ii−i−i11-1-1iiii−i−i−i−i−ii−ii1-1i−iii−i−i-1-111-1-11111-1-1-11−ii-11−ii
χ191-11-11-11-1-11-1-1-1111iiii−i−i−i−i1111-1-1-1-11-1-111−i−iiiii−i−iii−i−i-1ii−i−i11-1-1iiii−i−i−i−ii−ii−i-11−ii−i−iii11-1-111-1-1-1-111-11−ii-11−ii
χ201-11-11-11-1-11-1-1-1111iiii−i−i−i−i1111-1-1-1-11-1-111−i−iii−i−iii−i−iii-1ii−i−i11-1-1iiii−i−i−i−i−ii−ii-11−ii−i−iii-1-111-1-111-1-1111-1i−i1-1i−i
χ211-11-11-11-1-11-1-1-1111iiii−i−i−i−i-1-1-1-11111111-1-1ii−i−iii−i−i−i−iii-1ii−i−i-1-111−i−i−i−iiiii−iii−i1-1i−i−i−iii11-1-1-1-111-1-111-11−ii1-1i−i
χ221-11-11-11-1-11-1-1-1111iiii−i−i−i−i-1-1-1-11111111-1-1ii−i−i−i−iiiii−i−i-1ii−i−i-1-111−i−i−i−iiiiii−i−ii1-1i−i−i−iii-1-11111-1-1-1-1111-1i−i-11−ii
χ231-11-11-11-1-11-1-1-1111iiii−i−i−i−i-1-1-1-111111-1-111−i−iiiii−i−i−i−iii-1ii−i−i-1-111−i−i−i−iiiii−iii−i-11−iiii−i−i11-1-1-1-11111-1-11-1i−i-11−ii
χ241-11-11-11-1-11-1-1-1111iiii−i−i−i−i-1-1-1-111111-1-111−i−iii−i−iiiii−i−i-1ii−i−i-1-111−i−i−i−iiiiii−i−ii-11−iiii−i−i-1-11111-1-111-1-1-11−ii1-1i−i
χ251-11-11-11-1-11-1-1-1111−i−i−i−iiiii1111-1-1-1-1111-1-1−i−iiiii−i−iii−i−i-1−i−iii11-1-1−i−i−i−iiiiii−ii−i1-1−ii−i−iii-1-111-1-11111-1-1-11i−i-11i−i
χ261-11-11-11-1-11-1-1-1111−i−i−i−iiiii1111-1-1-1-1111-1-1−i−iii−i−iii−i−iii-1−i−iii11-1-1−i−i−i−iiiii−ii−ii1-1−ii−i−iii11-1-111-1-111-1-11-1−ii1-1−ii
χ271-11-11-11-1-11-1-1-1111−i−i−i−iiiii1111-1-1-1-11-1-111ii−i−iii−i−iii−i−i-1−i−iii11-1-1−i−i−i−iiiiii−ii−i-11i−iii−i−i-1-111-1-111-1-1111-1−ii1-1−ii
χ281-11-11-11-1-11-1-1-1111−i−i−i−iiiii1111-1-1-1-11-1-111ii−i−i−i−iii−i−iii-1−i−iii11-1-1−i−i−i−iiiii−ii−ii-11i−iii−i−i11-1-111-1-1-1-111-11i−i-11i−i
χ291-11-11-11-1-11-1-1-1111−i−i−i−iiiii-1-1-1-11111111-1-1−i−iiiii−i−i−i−iii-1−i−iii-1-111iiii−i−i−i−i−iii−i1-1−iiii−i−i-1-11111-1-1-1-1111-1−ii-11i−i
χ301-11-11-11-1-11-1-1-1111−i−i−i−iiiii-1-1-1-11111111-1-1−i−iii−i−iiiii−i−i-1−i−iii-1-111iiii−i−i−i−ii−i−ii1-1−iiii−i−i11-1-1-1-111-1-111-11i−i1-1−ii
χ311-11-11-11-1-11-1-1-1111−i−i−i−iiiii-1-1-1-111111-1-111ii−i−iii−i−i−i−iii-1−i−iii-1-111iiii−i−i−i−i−iii−i-11i−i−i−iii-1-11111-1-111-1-1-11i−i1-1−ii
χ321-11-11-11-1-11-1-1-1111−i−i−i−iiiii-1-1-1-111111-1-111ii−i−i−i−iiiii−i−i-1−i−iii-1-111iiii−i−i−i−ii−i−ii-11i−i−i−iii11-1-1-1-11111-1-11-1−ii-11i−i
χ332222222222-2-22-2-220000000022222222-20000000022222222-20000-2-2-2-200000000-2-2-2-20000000000000000000000000000
χ342222222222-2-22-2-220000000022222222-200000000-2-2-2-2-2-2-2-2-20000-2-2-2-20000000022220000000000000000000000000000
χ352222222222-2-22-2-2200000000-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2-2000022220000000022-2-20000000000000000000000000000
χ362222222222-2-22-2-2200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-22222-20000222200000000-2-2220000000000000000000000000000
χ3722222222-2-222-222-22222222200000000-22222222200000000-2-2-2-2-20000000000000000-2-2-2-2000000000000000000000000
χ3822222222-2-222-222-22222222200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-2-200000000000000002222000000000000000000000000
χ3922222222-2-222-222-2-2-2-2-2-2-2-2-200000000-22222-2-2-2-200000000-222220000000000000000-2-222000000000000000000000000
χ4022222222-2-222-222-2-2-2-2-2-2-2-2-200000000-2-2-2-2-2222200000000-22222000000000000000022-2-2000000000000000000000000
χ4122-2-222-2-2-2-200200222−2−222−2−22i2i−2i−2i2i2i−2i−2i0000000002-22-22i−2i2i−2i02−22−20000i2i2−i2−i2i2i2−i2−i20000000000002−22−2i2−i2i2−i2000000000000
χ4222-2-222-2-2-2-200200222−2−222−2−22i2i−2i−2i2i2i−2i−2i000000000-22-22−2i2i−2i2i02−22−20000i2i2−i2−i2i2i2−i2−i2000000000000−22−22−i2i2−i2i2000000000000
χ4322-2-222-2-2-2-200200222−2−222−2−2−2i−2i2i2i−2i−2i2i2i0000000002-22-2−2i2i−2i2i02−22−20000−i2−i2i2i2−i2−i2i2i20000000000002−22−2−i2i2−i2i2000000000000
χ4422-2-222-2-2-2-200200222−2−222−2−2−2i−2i2i2i−2i−2i2i2i000000000-22-222i−2i2i−2i02−22−20000−i2−i2i2i2−i2−i2i2i2000000000000−22−22i2−i2i2−i2000000000000
χ4522-2-222-2-2-2-2002002−2−222−2−2222i2i−2i−2i2i2i−2i−2i0000000002-22-22i−2i2i−2i0−22−220000−i2−i2i2i2−i2−i2i2i2000000000000−22−22−i2i2−i2i2000000000000
χ4622-2-222-2-2-2-2002002−2−222−2−2222i2i−2i−2i2i2i−2i−2i000000000-22-22−2i2i−2i2i0−22−220000−i2−i2i2i2−i2−i2i2i20000000000002−22−2i2−i2i2−i2000000000000
χ4722-2-222-2-2-2-2002002−2−222−2−222−2i−2i2i2i−2i−2i2i2i0000000002-22-2−2i2i−2i2i0−22−220000i2i2−i2−i2i2i2−i2−i2000000000000−22−22i2−i2i2−i2000000000000
χ4822-2-222-2-2-2-2002002−2−222−2−222−2i−2i2i2i−2i−2i2i2i000000000-22-222i−2i2i−2i0−22−220000i2i2−i2−i2i2i2−i2−i20000000000002−22−2−i2i2−i2i2000000000000
χ4922-2-2-2-222002-202-202-22-22-22-2i2−i2i2−i2i2−i2i2−i202i−2i2i−2i2i−2i2i−2i0000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000002−22−2000000002−22−200000000
χ5022-2-2-2-222002-202-202-22-22-22-2i2−i2i2−i2i2−i2i2−i20−2i2i−2i2i−2i2i−2i2i0000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000−22−2200000000−22−2200000000
χ5122-2-2-2-222002-202-202-22-22-22-2−i2i2−i2i2−i2i2−i2i202i−2i2i−2i2i−2i2i−2i0000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000−22−2200000000−22−2200000000
χ5222-2-2-2-222002-202-202-22-22-22-2−i2i2−i2i2−i2i2−i2i20−2i2i−2i2i−2i2i−2i2i0000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000002−22−2000000002−22−200000000
χ5322-2-2-2-222002-202-20-22-22-22-22i2−i2i2−i2i2−i2i2−i202i−2i2i−2i−2i2i−2i2i0000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000−22−22000000002−22−200000000
χ5422-2-2-2-222002-202-20-22-22-22-22i2−i2i2−i2i2−i2i2−i20−2i2i−2i2i2i−2i2i−2i0000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000002−22−200000000−22−2200000000
χ5522-2-2-2-222002-202-20-22-22-22-22−i2i2−i2i2−i2i2−i2i202i−2i2i−2i−2i2i−2i2i0000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000002−22−200000000−22−2200000000
χ5622-2-2-2-222002-202-20-22-22-22-22−i2i2−i2i2−i2i2−i2i20−2i2i−2i2i2i−2i2i−2i0000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000−22−22000000002−22−200000000
χ572-22-22-22-22-2-2-2222-22i2i2i2i−2i−2i−2i−2i00000000-222-2-22i2i−2i−2i000000002−2i−2i2i2i0000000000000000-22−2i2i000000000000000000000000
χ582-22-22-22-22-2-2-2222-22i2i2i2i−2i−2i−2i−2i00000000-2-2-222−2i−2i2i2i000000002−2i−2i2i2i00000000000000002-22i−2i000000000000000000000000
χ592-22-22-22-22-2-2-2222-2−2i−2i−2i−2i2i2i2i2i00000000-222-2-2−2i−2i2i2i0000000022i2i−2i−2i0000000000000000-222i−2i000000000000000000000000
χ602-22-22-22-22-2-2-2222-2−2i−2i−2i−2i2i2i2i2i00000000-2-2-2222i2i−2i−2i0000000022i2i−2i−2i00000000000000002-2−2i2i000000000000000000000000
χ612-22-22-22-2-2222-2-2-22000000002222-2-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i20000-2-22200000000−2i2i−2i2i0000000000000000000000000000
χ622-22-22-22-2-2222-2-2-22000000002222-2-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i20000-2-222000000002i−2i2i−2i0000000000000000000000000000
χ632-22-22-22-2-2222-2-2-2200000000-2-2-2-22222-2000000002i2i−2i−2i−2i−2i2i2i2000022-2-2000000002i−2i−2i2i0000000000000000000000000000
χ642-22-22-22-2-2222-2-2-2200000000-2-2-2-22222-200000000−2i−2i2i2i2i2i−2i−2i2000022-2-200000000−2i2i2i−2i0000000000000000000000000000
χ652-2-222-2-222-200-2002i2i2−i2−i2−i2−i2i2i22i2i−2i−2i−2i−2i2i2i0000000002i−2i−2i2i-222-20i2−i2−i2i20000−2−22222−2−20000000000002−2−22i2−i2−i2i2000000000000
χ662-2-222-2-222-200-2002i2i2−i2−i2−i2−i2i2i22i2i−2i−2i−2i−2i2i2i000000000−2i2i2i−2i2-2-220i2−i2−i2i20000−2−22222−2−2000000000000−222−2−i2i2i2−i2000000000000
χ672-2-222-2-222-200-2002i2i2−i2−i2−i2−i2i2i2−2i−2i2i2i2i2i−2i−2i0000000002i−2i−2i2i2-2-220i2−i2−i2i2000022−2−2−2−2220000000000002−2−22−i2i2i2−i2000000000000
χ682-2-222-2-222-200-2002i2i2−i2−i2−i2−i2i2i2−2i−2i2i2i2i2i−2i−2i000000000−2i2i2i−2i-222-20i2−i2−i2i2000022−2−2−2−222000000000000−222−2i2−i2−i2i2000000000000
χ692-2-222-2-222-200-2002−i2−i2i2i2i2i2−i2−i22i2i−2i−2i−2i−2i2i2i0000000002i−2i−2i2i-222-20−i2i2i2−i2000022−2−2−2−222000000000000−222−2−i2i2i2−i2000000000000
χ702-2-222-2-222-200-2002−i2−i2i2i2i2i2−i2−i22i2i−2i−2i−2i−2i2i2i000000000−2i2i2i−2i2-2-220−i2i2i2−i2000022−2−2−2−2220000000000002−2−22i2−i2−i2i2000000000000
χ712-2-222-2-222-200-2002−i2−i2i2i2i2i2−i2−i2−2i−2i2i2i2i2i−2i−2i0000000002i−2i−2i2i2-2-220−i2i2i2−i20000−2−22222−2−2000000000000−222−2i2−i2−i2i2000000000000
χ722-2-222-2-222-200-2002−i2−i2i2i2i2i2−i2−i2−2i−2i2i2i2i2i−2i−2i000000000−2i2i2i−2i-222-20−i2i2i2−i20000−2−22222−2−20000000000002−2−22−i2i2i2−i2000000000000
χ732-2-22-222-200-2202-202i−2i2i−2i−2i2i−2i2ii2−i2i2−i2−i2i2−i2i202i−2i−2i2i-222-20000000000000i2−i2−i2i2−22−222−22−200000000i2−i2−i2i2000000002−2−2200000000
χ742-2-22-222-200-2202-202i−2i2i−2i−2i2i−2i2ii2−i2i2−i2−i2i2−i2i20−2i2i2i−2i2-2-220000000000000i2−i2−i2i2−22−222−22−200000000−i2i2i2−i200000000−222−200000000
χ752-2-22-222-200-2202-202i−2i2i−2i−2i2i−2i2i−i2i2−i2i2i2−i2i2−i202i−2i−2i2i-222-20000000000000−i2i2i2−i22−22−2−22−2200000000−i2i2i2−i200000000−222−200000000
χ762-2-22-222-200-2202-202i−2i2i−2i−2i2i−2i2i−i2i2−i2i2i2−i2i2−i20−2i2i2i−2i2-2-220000000000000−i2i2i2−i22−22−2−22−2200000000i2−i2−i2i2000000002−2−2200000000
χ772-2-22-222-200-2202-20−2i2i−2i2i2i−2i2i−2ii2−i2i2−i2−i2i2−i2i202i−2i−2i2i2-2-220000000000000i2−i2−i2i22−22−2−22−2200000000−i2i2i2−i2000000002−2−2200000000
χ782-2-22-222-200-2202-20−2i2i−2i2i2i−2i2i−2ii2−i2i2−i2−i2i2−i2i20−2i2i2i−2i-222-20000000000000i2−i2−i2i22−22−2−22−2200000000i2−i2−i2i200000000−222−200000000
χ792-2-22-222-200-2202-20−2i2i−2i2i2i−2i2i−2i−i2i2−i2i2i2−i2i2−i202i−2i−2i2i2-2-220000000000000−i2i2i2−i2−22−222−22−200000000i2−i2−i2i200000000−222−200000000
χ802-2-22-222-200-2202-20−2i2i−2i2i2i−2i2i−2i−i2i2−i2i2i2−i2i2−i20−2i2i2i−2i-222-20000000000000−i2i2i2−i2−22−222−22−200000000−i2i2i2−i2000000002−2−2200000000
χ8144444444-4-4-4-4-4-4-4-40000000000000000400000000000000004000000000000000000000000000000000000000000000000
χ824444-4-4-4-40000000022−22−222222−22−222222−22−222222−22−2222000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ834444-4-4-4-40000000022−22−222222−22−2222−222222−22−222222−2200000000000000000000000000-222-2-222-200000000000000000000000000000000
χ844444-4-4-4-400000000−222222−22−222222−2222−22−222222−22−222200000000000000000000000000-222-2-222-200000000000000000000000000000000
χ854444-4-4-4-400000000−222222−22−222222−22−222222−22−222222−22000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ8644-4-444-4-44400-400-42222−22−222222−22−2200000000000000000000000000−2222−222200000000000000000000000000000000000000000000
χ8744-4-444-4-44400-400-4−22−222222−22−2222220000000000000000000000000022−2222−2200000000000000000000000000000000000000000000
χ8844-4-4-4-44400-440-440000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000−2i22i2−2i22i20000000000000000000000000000000000000000
χ8944-4-4-4-44400-440-44000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000002i2−2i22i2−2i20000000000000000000000000000000000000000
χ904-44-44-44-44-4444-4-4-4000000000000000040000000000000000-4000000000000000000000000000000000000000000000000
χ914-44-4-44-44000000002i2−2i2−2i22i2−2i22i22i2−2i222−22−2222−222222−22000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ924-44-4-44-44000000002i2−2i2−2i22i2−2i22i22i2−2i2−222222−2222−22−222200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ934-44-4-44-4400000000−2i22i22i2−2i22i2−2i2−2i22i222−22−2222−222222−2200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ944-44-4-44-4400000000−2i22i22i2−2i22i2−2i2−2i22i2−222222−2222−22−2222000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ954-4-444-4-44-4400400-42i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ964-4-444-4-44-4400400-4−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ974-4-44-444-4004-40-440000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ984-4-44-444-4004-40-44000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000

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