Finite Group Databasebeta

← Group #494913

Character table — Group #494913

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order122222222222444444448888888816161616161616161616161616161616444444448888888888881616161616161616161616161616161616161616161616162244444444444444
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
χ911111111-1-1-1-111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-111-1-1-1-111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ1711-11-1-11-111-1-11-111-1-11-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i11-1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-11-11-1i−ii−ii−ii−i1-11-1
χ1811-11-1-11-111-1-11-111-1-11-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i11-1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1-11-11−ii−ii−ii−ii-11-11
χ1911-11-1-11-111-1-11-111-1-11-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii11-1-1−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111-1-1-1-111111-11-1i−ii−i−ii−ii-11-11
χ2011-11-1-11-111-1-11-111-1-11-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii11-1-1−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111-1-1-1-11111-11-11−ii−iii−ii−i1-11-1
χ2111-11-1-11-111-1-11-111-1-11-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i11-1-1ii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-111111-11-1−ii−iii−ii−i-11-11
χ2211-11-1-11-111-1-11-111-1-11-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i11-1-1ii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-11-11i−ii−i−ii−ii1-11-1
χ2311-11-1-11-111-1-11-111-1-11-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii11-1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-11-11-1−ii−ii−ii−ii1-11-1
χ2411-11-1-11-111-1-11-111-1-11-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii11-1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1-11-11i−ii−ii−ii−i-11-11
χ2511-11-1-11-1-1-1111-1-1-1111-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i−i−iii-1-111ii−i−i−i−iii−i−i−i−iiiii1111-1-1-1-1-1-1-1-111111-1-11i−i−iii−i−ii1-1-11
χ2611-11-1-11-1-1-1111-1-1-1111-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i−i−iii-1-111ii−i−i−i−iii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-111-1−iii−i−iii−i-111-1
χ2711-11-1-11-1-1-1111-1-1-1111-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iiiii−i−i-1-111−i−iiiii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-11-1-11i−i−ii−iii−i-111-1
χ2811-11-1-11-1-1-1111-1-1-1111-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iiiii−i−i-1-111−i−iiiii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-111-1−iii−ii−i−ii1-1-11
χ2911-11-1-11-1-1-1111-1-1-1111-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−iii-1-111ii−i−i−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-11-1-11−iii−ii−i−ii-111-1
χ3011-11-1-11-1-1-1111-1-1-1111-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−iii-1-111ii−i−i−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1-111-1i−i−ii−iii−i1-1-11
χ3111-11-1-11-1-1-1111-1-1-1111-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iiiii−i−i-1-111−i−iiiii−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-111111-1-11−iii−i−iii−i1-1-11
χ3211-11-1-11-1-1-1111-1-1-1111-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iiiii−i−i-1-111−i−iiiii−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-111-1i−i−iii−i−ii-111-1
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
χ35222222222222-2-2-2-2-2-2-2-2000000002222−2−2−2−22222−2−2−2−22-22-22-22-200000000000022−2−222−2−222−2−222−2−222−2−222−2−20000000000000000
χ36222222222222-2-2-2-2-2-2-2-2000000002222−2−2−2−22222−2−2−2−2-22-22-22-2200000000000022−2−222−2−2−2−222−2−222−2−222−2−2220000000000000000
χ37222222222222-2-2-2-2-2-2-2-200000000−2−2−2−22222−2−2−2−222222-22-22-22-2000000000000−2−222−2−222−2−222−2−222−2−222−2−2220000000000000000
χ38222222222222-2-2-2-2-2-2-2-200000000−2−2−2−22222−2−2−2−22222-22-22-22-22000000000000−2−222−2−22222−2−222−2−222−2−222−2−20000000000000000
χ3922222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-200000000000000002222-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ4022222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2222222222222-2-2-2-20000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-22222-2-2000000002222−2−2−2−22222−2−2−2−22-22-2-22-22000000000000−2−222−2−22222−2−222−2−2−2−222−2−2220000000000000000
χ4222222222-2-2-2-2-2-22222-2-2000000002222−2−2−2−22222−2−2−2−2-22-222-22-2000000000000−2−222−2−222−2−222−2−22222−2−222−2−20000000000000000
χ4322222222-2-2-2-2-2-22222-2-200000000−2−2−2−22222−2−2−2−222222-22-2-22-2200000000000022−2−222−2−2−2−222−2−22222−2−222−2−20000000000000000
χ4422222222-2-2-2-2-2-22222-2-200000000−2−2−2−22222−2−2−2−22222-22-222-22-200000000000022−2−222−2−222−2−222−2−2−2−222−2−2220000000000000000
χ4522-22-2-22-222-2-22-222-2-22-2-2-222-2-22200000000000000002i2i−2i−2i2i2i−2i−2i-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ4622-22-2-22-222-2-22-222-2-22-2-2-222-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ4722-22-2-22-222-2-2-22-2-222-2200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22i−2i−2i2i2i−2i−2i2i000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−22222−2−2−2−2220000000000000000
χ4822-22-2-22-222-2-2-22-2-222-2200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2−2i2i2i−2i−2i2i2i−2i000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2−2−22222−2−20000000000000000
χ4922-22-2-22-222-2-2-22-2-222-2200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22i−2i−2i2i2i−2i−2i2i000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2−2−22222−2−20000000000000000
χ5022-22-2-22-222-2-2-22-2-222-2200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2−2i2i2i−2i−2i2i2i−2i000000000000−i2−i2i2i2i2i2−i2−i222−2−2−2−22222−2−2−2−2220000000000000000
χ5122-22-2-22-2-2-2222-2-2-2222-2-2-222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i22-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ5222-22-2-22-2-2-2222-2-2-2222-2-2-222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i22-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ5322-22-2-22-2-2-222-2222-2-2-2200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22i−2i−2i2i−2i2i2i−2i000000000000−i2−i2i2i2i2i2−i2−i222−2−2−2−222−2−22222−2−20000000000000000
χ5422-22-2-22-2-2-222-2222-2-2-2200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2−2i2i2i−2i2i−2i−2i2i000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−222−2−2−2−2220000000000000000
χ5522-22-2-22-2-2-222-2222-2-2-2200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22i−2i−2i2i−2i2i2i−2i000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−222−2−2−2−2220000000000000000
χ5622-22-2-22-2-2-222-2222-2-2-2200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2−2i2i2i−2i2i−2i−2i2i000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222−2−22222−2−20000000000000000
χ572-222-2-2-222-22-22-22-22-2-2200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000002-22-22-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ582-222-2-2-222-22-22-22-22-2-2200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000-22-22-22-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ592-222-2-2-222-22-22-22-22-2-2200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000002-22-22-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ602-222-2-2-222-22-22-22-22-2-2200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000-22-22-22-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ612-222-2-2-222-22-2-22-22-222-222-2-2-2-2220000000000000000000000002-22-200000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000
χ622-222-2-2-222-22-2-22-22-222-222-2-2-2-2220000000000000000000000002-22-20000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000
χ632-222-2-2-222-22-2-22-22-222-2-2-22222-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000-22-22000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ642-222-2-2-222-22-2-22-22-222-2-2-22222-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000-22-2200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ652-222-2-2-22-22-222-2-22-22-2200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000002-22-2-22-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ662-222-2-2-22-22-222-2-22-22-2200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000-22-222-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ672-222-2-2-22-22-222-2-22-22-2200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000002-22-2-22-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ682-222-2-2-22-22-222-2-22-22-2200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000-22-222-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ692-222-2-2-22-22-22-222-22-22-222-2-2-2-222000000000000000000000000-22-2200000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i0000000000000000
χ702-222-2-2-22-22-22-222-22-22-222-2-2-2-222000000000000000000000000-22-220000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i0000000000000000
χ712-222-2-2-22-22-22-222-22-22-2-2-22222-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000002-22-200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ722-222-2-2-22-22-22-222-22-22-2-2-22222-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000002-22-2000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ732-2-2222-2-22-2-22222-2-22-2-20000000022−2−222−2−2−2−222−2−2220000000000002i−2i−2i2i2i−2i−2i2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.