Finite Group Databasebeta

← Group #108191

Character table — Group #108191

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888888888888888888844444444444488888888
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111111-1-1−i−iiiii−i−i
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χ181-1-11-1-11111-1-11111-1-1-1-1-1-1111-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii−ii−ii-11-11-11-11
χ191-1-11-1-11111-1-11111-1-1-1-1-1-1111-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−ii−ii−i-11-11-11-11
χ201-1-11-1-11111-1-11111-1-1-1-1-1-1111-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii−ii−ii1-11-11-11-1
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χ241-1-11-1-11111-1-11111-1-1-1-1-1-1111-111-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iiii−ii−i1-11-1-11-11
χ251-1-11-1-11111-1-1-1-1-1-1111111-1-1-1111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiii−i−ii−iii−i−iii−i
χ261-1-11-1-11111-1-1-1-1-1-1111111-1-1-1111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−iii−ii−i−iii−i−ii
χ271-1-11-1-11111-1-1-1-1-1-1111111-1-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiii−i−iii−i−iii−i−ii
χ281-1-11-1-11111-1-1-1-1-1-1111111-1-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−iii−i−iii−i−iii−i
χ291-1-11-1-11111-1-1-1-1-1-1111111-1-1-1111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−iii−i−iii−ii−i−ii
χ301-1-11-1-11111-1-1-1-1-1-1111111-1-1-1111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−ii−i−iii−i−ii−iii−i
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χ321-1-11-1-11111-1-1-1-1-1-1111111-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−ii−i−ii−iii−ii−i−ii
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χ852-2-2-2222-2-222-200-222-2-22002-20000002i−2i00−2i2i0000−2i2i002i−2ii2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i22−2−22−222−2−222−22−2−2200000000000000000000
χ862-2-2-2222-2-222-200-222-2-22002-20000002i−2i00−2i2i0000−2i2i002i−2i−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−222−22−2−222−2−22−222−200000000000000000000
χ872-2-2-2222-2-222-200-222-2-22002-2000000−2i2i002i−2i00002i−2i00−2i2ii2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−222−22−2−222−2−22−222−200000000000000000000
χ882-2-2-2222-2-222-200-222-2-22002-2000000−2i2i002i−2i00002i−2i00−2i2i−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i22−2−22−222−2−222−22−2−2200000000000000000000
χ8944-4-44-4-4400004i−4i0000004i−4i000000000000000000000000000000000000000000000000000000002-22-22i−2i2i−2i000000000000
χ9044-4-44-4-4400004i−4i0000004i−4i00000000000000000000000000000000000000000000000000000000-22-22−2i2i−2i2i000000000000
χ9144-4-44-4-440000−4i4i000000−4i4i000000000000000000000000000000000000000000000000000000002-22-2−2i2i−2i2i000000000000
χ9244-4-44-4-440000−4i4i000000−4i4i00000000000000000000000000000000000000000000000000000000-22-222i−2i2i−2i000000000000
χ934-44-4-44-4400004i−4i000000−4i4i000000000000000000000000000000000000000000000000000000002i−2i−2i2i-222-2000000000000
χ944-44-4-44-4400004i−4i000000−4i4i00000000000000000000000000000000000000000000000000000000−2i2i2i−2i2-2-22000000000000
χ954-44-4-44-440000−4i4i0000004i−4i000000000000000000000000000000000000000000000000000000002i−2i−2i2i2-2-22000000000000
χ964-44-4-44-440000−4i4i0000004i−4i00000000000000000000000000000000000000000000000000000000−2i2i2i−2i-222-2000000000000
χ9788-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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