Finite Group Databasebeta

← Group #189214

Character table — Group #189214

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12224444222244444444444422222444444444444444448888888888888888888888888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ91111111111-1-111-1-1-1-1-1-11111-1111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111-1-111-1-1-1-1-1-11111-1111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ111111111111-1-111-1-1-1-1-1-11111-1111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-111
χ121111111111-1-111-1-1-1-1-1-11111-1111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-111-1-1
χ131111111111-1-111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1
χ141111111111-1-111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-111
χ151111111111-1-111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ161111111111-1-111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ171111-1-1-1-1-1-1111111-1-1-1-11-1-11-111-1-11-111-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−ii−ii−ii−ii−ii−i
χ181111-1-1-1-1-1-1111111-1-1-1-11-1-11-111-1-11-111-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−ii−ii−ii−ii−ii
χ191111-1-1-1-1-1-1111111-1-1-1-11-1-11-111-1-11-111-111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111ii−i−iii−i−ii−ii−i−ii−ii−ii−ii
χ201111-1-1-1-1-1-1111111-1-1-1-11-1-11-111-1-11-111-111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111−i−iii−i−iii−ii−iii−ii−ii−ii−i
χ211111-1-1-1-1-1-1111111-1-1-1-11-1-11-1-1-1111-111-1-1-111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−ii−ii−ii−iii−ii−i
χ221111-1-1-1-1-1-1111111-1-1-1-11-1-11-1-1-1111-111-1-1-111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiii−ii−ii−ii−i−ii−ii
χ231111-1-1-1-1-1-1111111-1-1-1-11-1-11-1-1-1111-111-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1ii−i−iii−i−i−ii−iii−ii−i−ii−ii
χ241111-1-1-1-1-1-1111111-1-1-1-11-1-11-1-1-1111-111-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−iii−i−iiii−ii−i−ii−iii−ii−i
χ251111-1-1-1-1-1-1-1-111-1-111111-1-11111-1-11-1-1-1111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiii−i−iii−i−iii−i−ii
χ261111-1-1-1-1-1-1-1-111-1-111111-1-11111-1-11-1-1-1111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−iii−i−iii−i−iii−i
χ271111-1-1-1-1-1-1-1-111-1-111111-1-11111-1-11-1-1-1111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiii−i−ii−iii−i−iii−i
χ281111-1-1-1-1-1-1-1-111-1-111111-1-11111-1-11-1-1-1111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−iii−ii−i−iii−i−ii
χ291111-1-1-1-1-1-1-1-111-1-111111-1-111-1-1111-1-1-11-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−iii−i−iii−ii−i−ii
χ301111-1-1-1-1-1-1-1-111-1-111111-1-111-1-1111-1-1-11-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1−i−iiiii−i−ii−i−iii−i−ii−iii−i
χ311111-1-1-1-1-1-1-1-111-1-111111-1-111-1-1111-1-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−iii−ii−i−ii−iii−i
χ321111-1-1-1-1-1-1-1-111-1-111111-1-111-1-1111-1-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−ii−i−ii−iii−ii−i−ii
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χ4222222222-2-2-2-222-2-2-2-2-2-2-222-22-2-222-2-222222-2-222-2-222-2-20000000000000000000000000000000000000000000000000000
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χ8122-2-2−2i2i−2i2i00-222-2-222i−2i2i−2i0−2i2i00002-200000−2i2i00002i−2i00-22i2−i2−22−i2i22−2i2−i2−22−i2i22−2−22−22i2−i2i2−i22−22−2−i2i2−i2i200000000000000000000
χ8222-2-2−2i2i−2i2i00-222-2-222i−2i2i−2i0−2i2i00002-200000−2i2i00002i−2i00-22−i2i22−2i2−i2−22−i2i22−2i2−i2−222−22−2−i2i2−i2i2−22−22i2−i2i2−i200000000000000000000
χ8322-2-2−2i2i−2i2i00-222-2-222i−2i2i−2i0−2i2i0000-22000002i−2i0000−2i2i002-2i2−i2−22−i2i22−2i2−i2−22−i2i22−22−22−2−i2i2−i2i2−22−22i2−i2i2−i200000000000000000000
χ8422-2-2−2i2i−2i2i00-222-2-222i−2i2i−2i0−2i2i0000-22000002i−2i0000−2i2i002-2−i2i22−2i2−i2−22−i2i22−2i2−i2−22−22−22i2−i2i2−i22−22−2−i2i2−i2i200000000000000000000
χ8522-2-2−2i2i−2i2i00-22-222-22i−2i−2i2i02i−2i002-2000000000−2i2i-22002i−2i00i2−i2−22i2−i2−22−i2i22−2−i2i22−2i2−i2−i2i22−2−22−i2i2i2−i2−222−200000000000000000000
χ8622-2-2−2i2i−2i2i00-22-222-22i−2i−2i2i02i−2i002-2000000000−2i2i-22002i−2i00−i2i22−2−i2i22−2i2−i2−22i2−i2−22−i2i2i2−i2−222−2i2−i2−i2i22−2−2200000000000000000000
χ8722-2-2−2i2i−2i2i00-22-222-22i−2i−2i2i02i−2i00-220000000002i−2i2-200−2i2i00i2−i2−22i2−i2−22−i2i22−2−i2i22−2−i2i2i2−i2−222−2i2−i2−i2i22−2−2200000000000000000000
χ8822-2-2−2i2i−2i2i00-22-222-22i−2i−2i2i02i−2i00-220000000002i−2i2-200−2i2i00−i2i22−2−i2i22−2i2−i2−22i2−i2−22i2−i2−i2i22−2−22−i2i2i2−i2−222−200000000000000000000
χ894-44-444-4-44-40000000000400-400000000000000000000000000000000000000000000000000000022−2222−220000000000000000
χ904-44-444-4-44-40000000000400-4000000000000000000000000000000000000000000000000000000−2222−22220000000000000000
χ914-44-444-4-4-440000000000-400400000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ924-44-444-4-4-440000000000-40040000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ934-44-4-4-4444-40000000000-4004000000000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ944-44-4-4-4444-40000000000-40040000000000000000000000000000000000000000000000000000000000−222222−22000000000000
χ954-44-4-4-444-440000000000400-40000000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ964-44-4-4-444-440000000000400-4000000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ978-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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