Finite Group Databasebeta

← Group #495859

Character table — Group #495859

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order122222224444444444448888888816161616161616161616161616161616224444448888888888881616161616161616161616161616161616161616161616164444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-111-1-1-1-111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ1711-1-11-11-1ii−i−i1-1ii−i−i1-111-1-111-1-111111111-1-1-1-1-1-1-1-11-1i−i1-1i−iii−i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i1-1i−i1-1i−i1-1i−i
χ1811-1-11-11-1ii−i−i1-1ii−i−i1-111-1-111-1-111111111-1-1-1-1-1-1-1-11-1i−i1-1i−iii−i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii-11−ii-11−ii-11−ii
χ1911-1-11-11-1ii−i−i1-1ii−i−i1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-11−ii-11−iiii−i−i-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1i−i1-1i−i-11−ii-11−ii
χ2011-1-11-11-1ii−i−i1-1ii−i−i1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-11−ii-11−iiii−i−i-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11−ii-11−ii1-1i−i1-1i−i
χ2111-1-11-11-1ii−i−i1-1ii−i−i1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1i−i1-1i−iii−i−i11-1-1ii−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii1-1i−i-11−ii1-1i−i-11−ii
χ2211-1-11-11-1ii−i−i1-1ii−i−i1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1i−i1-1i−iii−i−i11-1-1ii−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-11−ii1-1i−i-11−ii1-1i−i
χ2311-1-11-11-1ii−i−i1-1ii−i−i1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-11−ii-11−iiii−i−i-1-111−i−iii−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i1-1i−i-11−ii-11−ii1-1i−i
χ2411-1-11-11-1ii−i−i1-1ii−i−i1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-11−ii-11−iiii−i−i-1-111−i−iii−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-11−ii1-1i−i1-1i−i-11−ii
χ2511-1-11-11-1−i−iii1-1−i−iii1-111-1-111-1-111111111-1-1-1-1-1-1-1-11-1−ii1-1−ii−i−iii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-1−ii1-1−ii1-1−ii1-1−ii
χ2611-1-11-11-1−i−iii1-1−i−iii1-111-1-111-1-111111111-1-1-1-1-1-1-1-11-1−ii1-1−ii−i−iii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11i−i-11i−i-11i−i-11i−i
χ2711-1-11-11-1−i−iii1-1−i−iii1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-11i−i-11i−i−i−iii-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1−ii1-1−ii-11i−i-11i−i
χ2811-1-11-11-1−i−iii1-1−i−iii1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-11i−i-11i−i−i−iii-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11i−i-11i−i1-1−ii1-1−ii
χ2911-1-11-11-1−i−iii1-1−i−iii1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1−ii1-1−ii−i−iii11-1-1−i−iiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i1-1−ii-11i−i1-1−ii-11i−i
χ3011-1-11-11-1−i−iii1-1−i−iii1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1−ii1-1−ii−i−iii11-1-1−i−iiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-11i−i1-1−ii-11i−i1-1−ii
χ3111-1-11-11-1−i−iii1-1−i−iii1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-11i−i-11i−i−i−iii-1-111ii−i−iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii1-1−ii-11i−i-11i−i1-1−ii
χ3211-1-11-11-1−i−iii1-1−i−iii1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-11i−i-11i−i−i−iii-1-111ii−i−iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-11i−i1-1−ii1-1−ii-11i−i
χ3322222222222222222222-2-2-2-2-2-2-2-2000000000000000022222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2000000002222−2−2−2−22222−2−2−2−222-2-2-2-22200000000000022−2−222−2−222−2−222−2−222−2−222−2−20000000000000000
χ36222222222222-2-2-2-2-2-2-2-2000000002222−2−2−2−22222−2−2−2−2-2-22222-2-200000000000022−2−222−2−2−2−222−2−222−2−222−2−2220000000000000000
χ37222222222222-2-2-2-2-2-2-2-200000000−2−2−2−22222−2−2−2−2222222-2-2-2-222000000000000−2−222−2−222−2−222−2−222−2−222−2−2220000000000000000
χ38222222222222-2-2-2-2-2-2-2-200000000−2−2−2−22222−2−2−2−22222-2-22222-2-2000000000000−2−222−2−22222−2−222−2−222−2−222−2−20000000000000000
χ3922222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-2000000000000000022-2-222-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ4022222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-20000000000000000-2-222-2-22222222222-2-2-2-20000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-22222-2-2000000002222−2−2−2−22222−2−2−2−22222-2-2-2-2000000000000−2−222−2−22222−2−222−2−2−2−222−2−2220000000000000000
χ4222222222-2-2-2-2-2-22222-2-2000000002222−2−2−2−22222−2−2−2−2-2-2-2-22222000000000000−2−222−2−222−2−222−2−22222−2−222−2−20000000000000000
χ4322222222-2-2-2-2-2-22222-2-200000000−2−2−2−22222−2−2−2−222222222-2-2-2-200000000000022−2−222−2−2−2−222−2−22222−2−222−2−20000000000000000
χ4422222222-2-2-2-2-2-22222-2-200000000−2−2−2−22222−2−2−2−22222-2-2-2-2222200000000000022−2−222−2−222−2−222−2−2−2−222−2−2220000000000000000
χ4522-2-22-22-22i2i−2i−2i2-22i2i−2i−2i2-2-2-222-2-22200000000000000002-22i−2i2-22i−2i−2i−2i2i2i-2-222−2i−2i2i2i0000000000000000000000000000000000000000
χ4622-2-22-22-22i2i−2i−2i2-22i2i−2i−2i2-2-2-222-2-2220000000000000000-22−2i2i-22−2i2i−2i−2i2i2i22-2-22i2i−2i−2i0000000000000000000000000000000000000000
χ4722-2-22-22-22i2i−2i−2i-22−2i−2i2i2i-22000000002222−2−2−2−2−2−2−2−222222-2−2i2i-222i−2i000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ4822-2-22-22-22i2i−2i−2i-22−2i−2i2i2i-22000000002222−2−2−2−2−2−2−2−22222-222i−2i2-2−2i2i000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ4922-2-22-22-22i2i−2i−2i-22−2i−2i2i2i-2200000000−2−2−2−222222222−2−2−2−22-2−2i2i-222i−2i000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ5022-2-22-22-22i2i−2i−2i-22−2i−2i2i2i-2200000000−2−2−2−222222222−2−2−2−2-222i−2i2-2−2i2i000000000000−i2−i2i2i2i2i2−i2−i222−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ5122-2-22-22-2−2i−2i2i2i2-2−2i−2i2i2i2-2-2-222-2-22200000000000000002-2−2i2i2-2−2i2i2i2i−2i−2i-2-2222i2i−2i−2i0000000000000000000000000000000000000000
χ5222-2-22-22-2−2i−2i2i2i2-2−2i−2i2i2i2-2-2-222-2-2220000000000000000-222i−2i-222i−2i2i2i−2i−2i22-2-2−2i−2i2i2i0000000000000000000000000000000000000000
χ5322-2-22-22-2−2i−2i2i2i-222i2i−2i−2i-22000000002222−2−2−2−2−2−2−2−222222-22i−2i-22−2i2i000000000000−i2−i2i2i2i2i2−i2−i222−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ5422-2-22-22-2−2i−2i2i2i-222i2i−2i−2i-22000000002222−2−2−2−2−2−2−2−22222-22−2i2i2-22i−2i000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ5522-2-22-22-2−2i−2i2i2i-222i2i−2i−2i-2200000000−2−2−2−222222222−2−2−2−22-22i−2i-22−2i2i000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ5622-2-22-22-2−2i−2i2i2i-222i2i−2i−2i-2200000000−2−2−2−222222222−2−2−2−2-22−2i2i2-22i−2i000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ572-22-2-222-22i−2i2i−2i2-22i−2i2i−2i-220000000022−2−222−2−222−2−222−2−20000000000002i−2i2i−2i2-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ582-22-2-222-22i−2i2i−2i2-22i−2i2i−2i-220000000022−2−222−2−222−2−222−2−2000000000000−2i2i−2i2i-22-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ592-22-2-222-22i−2i2i−2i2-22i−2i2i−2i-2200000000−2−222−2−222−2−222−2−2220000000000002i−2i2i−2i2-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ602-22-2-222-22i−2i2i−2i2-22i−2i2i−2i-2200000000−2−222−2−222−2−222−2−222000000000000−2i2i−2i2i-22-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ612-22-2-222-22i−2i2i−2i-22−2i2i−2i2i2-222-2-2-2-2220000000000000000000000002i−2i2i−2i00000000000000002i−2i−2i2i2i−2i−2i2i2-2-222-2-220000000000000000
χ622-22-2-222-22i−2i2i−2i-22−2i2i−2i2i2-222-2-2-2-2220000000000000000000000002i−2i2i−2i0000000000000000−2i2i2i−2i−2i2i2i−2i-222-2-222-20000000000000000
χ632-22-2-222-22i−2i2i−2i-22−2i2i−2i2i2-2-2-22222-2-222-2-2-2-22222-2-2-2-22200000000−2i2i−2i2i000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ642-22-2-222-22i−2i2i−2i-22−2i2i−2i2i2-2-2-22222-2-2-2-22222-2-2-2-22222-2-200000000−2i2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ652-22-2-222-2−2i2i−2i2i2-2−2i2i−2i2i-220000000022−2−222−2−222−2−222−2−20000000000002i−2i2i−2i-22-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ662-22-2-222-2−2i2i−2i2i2-2−2i2i−2i2i-220000000022−2−222−2−222−2−222−2−2000000000000−2i2i−2i2i2-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ672-22-2-222-2−2i2i−2i2i2-2−2i2i−2i2i-2200000000−2−222−2−222−2−222−2−2220000000000002i−2i2i−2i-22-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ682-22-2-222-2−2i2i−2i2i2-2−2i2i−2i2i-2200000000−2−222−2−222−2−222−2−222000000000000−2i2i−2i2i2-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ692-22-2-222-2−2i2i−2i2i-222i−2i2i−2i2-222-2-2-2-222000000000000000000000000−2i2i−2i2i00000000000000002i−2i−2i2i2i−2i−2i2i-222-2-222-20000000000000000
χ702-22-2-222-2−2i2i−2i2i-222i−2i2i−2i2-222-2-2-2-222000000000000000000000000−2i2i−2i2i0000000000000000−2i2i2i−2i−2i2i2i−2i2-2-222-2-220000000000000000
χ712-22-2-222-2−2i2i−2i2i-222i−2i2i−2i2-2-2-22222-2-222-2-2-2-22222-2-2-2-222000000002i−2i2i−2i00000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ722-22-2-222-2−2i2i−2i2i-222i−2i2i−2i2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2000000002i−2i2i−2i000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ732-2-22-2-2222-2-22222-2-22-2-20000000022−2−222−2−2−2−222−2−2220000000000002i−2i−2i2i−2i2i2i−2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.