Finite Group Databasebeta

← Group #197863

Character table — Group #197863

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222222244444444444422224444444444444444448888888888888888888888888888888888888888444444448888
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
χ5111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1
χ1411111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-111
χ1511111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
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χ181-1-111-1-1111-1-11-111-1-111-11-1-111-1-11-11-11111-1-1-1-11-111-1-1ii−i−iii−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii−ii−ii-11-11-11-11
χ191-1-111-1-1111-1-11-111-1-111-11-1-111-1-11-11-11111-1-1-1-11-111-1-1−i−iii−i−iii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−ii−ii−i-11-11-11-11
χ201-1-111-1-1111-1-11-111-1-111-11-1-111-1-11-11-11111-1-1-1-11-111-1-1−i−iii−i−iii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii−ii−ii1-11-11-11-1
χ211-1-111-1-1111-1-11-111-1-111-11-1-1-1-1111-11-1-1-1-1-111111-1-1-111ii−i−iii−i−iii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i−ii−ii-11-111-11-1
χ221-1-111-1-1111-1-11-111-1-111-11-1-1-1-1111-11-1-1-1-1-111111-1-1-111ii−i−iii−i−iii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iiii−ii−i1-11-1-11-11
χ231-1-111-1-1111-1-11-111-1-111-11-1-1-1-1111-11-1-1-1-1-111111-1-1-111−i−iii−i−iii−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i−ii−ii1-11-1-11-11
χ241-1-111-1-1111-1-11-111-1-111-11-1-1-1-1111-11-1-1-1-1-111111-1-1-111−i−iii−i−iii−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iiii−ii−i-11-111-11-1
χ251-1-111-1-11-1-1111-1-1-11111-11-1-111-1-11-1-11-1-1-1-11111-1111-1-1ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iiii−i−ii1-1-111-1-11
χ261-1-111-1-11-1-1111-1-1-11111-11-1-111-1-11-1-11-1-1-1-11111-1111-1-1ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i−iii−i-111-1-111-1
χ271-1-111-1-11-1-1111-1-1-11111-11-1-111-1-11-1-11-1-1-1-11111-1111-1-1−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iiii−i−ii-111-1-111-1
χ281-1-111-1-11-1-1111-1-1-11111-11-1-111-1-11-1-11-1-1-1-11111-1111-1-1−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i−iii−i1-1-111-1-11
χ291-1-111-1-11-1-1111-1-1-11111-11-1-1-1-1111-1-111111-1-1-1-1-11-1-111ii−i−i−i−iiiii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii−iii−i-111-11-1-11
χ301-1-111-1-11-1-1111-1-1-11111-11-1-1-1-1111-1-111111-1-1-1-1-11-1-111ii−i−i−i−iiiii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−ii−i−ii1-1-11-111-1
χ311-1-111-1-11-1-1111-1-1-11111-11-1-1-1-1111-1-111111-1-1-1-1-11-1-111−i−iiiii−i−i−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii−iii−i1-1-11-111-1
χ321-1-111-1-11-1-1111-1-1-11111-11-1-1-1-1111-1-111111-1-1-1-1-11-1-111−i−iiiii−i−i−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−ii−i−ii-111-11-1-11
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χ4122222222-2-2-2-2-2-22222222-2-220000-2-22200000000-2-2000022222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-22222222-2-220000-2-22200000000-2-20000-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-22222-2-2-2-2-2-2000022-2-20000000022000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000
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χ452222-2-2-2-22-22-2222-22-2000-2-202-22-200002-2002-2000000002−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−200000000000000000000
χ462222-2-2-2-22-22-2222-22-2000-2-202-22-200002-2002-200000000−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−2200000000000000000000
χ472222-2-2-2-22-22-2222-22-2000-2-20-22-220000-2200-22000000002−22−22−22−22−22−22−22−2−22−22−22−22−22−22−22−2200000000000000000000
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χ852-2-22-222-2-222-2-222-2-220002-2000000000002i−2i00−2i2i00−2i2i2i−2ii2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i22−2−22−222−2−222−22−2−2200000000000000000000
χ862-2-22-222-2-222-2-222-2-220002-2000000000002i−2i00−2i2i00−2i2i2i−2i−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−222−22−2−222−2−22−222−200000000000000000000
χ872-2-22-222-2-222-2-222-2-220002-200000000000−2i2i002i−2i002i−2i−2i2ii2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−222−22−2−222−2−22−222−200000000000000000000
χ882-2-22-222-2-222-2-222-2-220002-200000000000−2i2i002i−2i002i−2i−2i2i−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i22−2−22−222−2−222−22−2−2200000000000000000000
χ8944-4-4-44-4400000000004-4400-400000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ9044-4-4-44-4400000000004-4400-40000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ9144-4-4-44-440000000000-44-400400000000000000000000000000000000000000000000000000000022−2222−220000000000000000
χ9244-4-4-44-440000000000-44-4004000000000000000000000000000000000000000000000000000000−2222−22220000000000000000
χ934-44-4-4-44400000000004-4-4004000000000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ944-44-4-4-44400000000004-4-40040000000000000000000000000000000000000000000000000000000000−222222−22000000000000
χ954-44-4-4-4440000000000-44400-40000000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ964-44-4-4-4440000000000-44400-4000000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ9788-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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