Finite Group Databasebeta

← Group #225613

Character table — Group #225613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888844444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ171-11-111-1-1-1-1-1111-111111-1-1-1-11111-1-1-1-1ii−i−iii−i−i-111-1-111-1-1111-1-111-1-11111-1-1-1-11-11-1i−ii−iii−i−iii−i−i11-1-111-1-1i−ii−ii−ii−i
χ181-11-111-1-1-1-1-1111-111111-1-1-1-11111-1-1-1-1ii−i−iii−i−i-1-1-111-1-111111-1-111-1-11111-1-1-1-1-11-11i−ii−iii−i−iii−i−i-1-111-1-111−ii−ii−ii−ii
χ191-11-111-1-1-1-1-1111-111111-1-1-1-11111-1-1-1-1−i−iii−i−iii-111-1-111-1-1111-1-111-1-11111-1-1-1-11-11-1−ii−ii−i−iii−i−iii11-1-111-1-1−ii−ii−ii−ii
χ201-11-111-1-1-1-1-1111-111111-1-1-1-11111-1-1-1-1−i−iii−i−iii-1-1-111-1-111111-1-111-1-11111-1-1-1-1-11-11−ii−ii−i−iii−i−iii-1-111-1-111i−ii−ii−ii−i
χ211-11-111-1-1-1-1-1111-111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i-111-1-1-1-1111-1-11111-1-1-1-1-1-111111-1-11i−ii−i−i−iii−i−iii11-1-1-1-111i−ii−i−ii−ii
χ221-11-111-1-1-1-1-1111-111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i-1-1-11111-1-11-1-11111-1-1-1-1-1-11111-111-1i−ii−i−i−iii−i−iii-1-11111-1-1−ii−iii−ii−i
χ231-11-111-1-1-1-1-1111-111111-1-1-1-1-1-1-1-11111−i−iii−i−iii-111-1-1-1-1111-1-11111-1-1-1-1-1-111111-1-11−ii−iiii−i−iii−i−i11-1-1-1-111−ii−iii−ii−i
χ241-11-111-1-1-1-1-1111-111111-1-1-1-1-1-1-1-11111−i−iii−i−iii-1-1-11111-1-11-1-11111-1-1-1-1-1-11111-111-1−ii−iiii−i−iii−i−i-1-11111-1-1i−ii−i−ii−ii
χ251-11-111-1-1-1-1-1111-11-1-1-1-111111111-1-1-1-1ii−i−i−i−iii-111-1-111-1-1111-1-1-1-111-1-1-1-111111-11-1i−i−iiii−i−i−i−iii-1-111-1-111i−i−iii−i−ii
χ261-11-111-1-1-1-1-1111-11-1-1-1-111111111-1-1-1-1ii−i−i−i−iii-1-1-111-1-111111-1-1-1-111-1-1-1-11111-11-11i−i−iiii−i−i−i−iii11-1-111-1-1−iii−i−iii−i
χ271-11-111-1-1-1-1-1111-11-1-1-1-111111111-1-1-1-1−i−iiiii−i−i-111-1-111-1-1111-1-1-1-111-1-1-1-111111-11-1−iii−i−i−iiiii−i−i-1-111-1-111−iii−i−iii−i
χ281-11-111-1-1-1-1-1111-11-1-1-1-111111111-1-1-1-1−i−iiiii−i−i-1-1-111-1-111111-1-1-1-111-1-1-1-11111-11-11−iii−i−i−iiiii−i−i11-1-111-1-1i−i−iii−i−ii
χ291-11-111-1-1-1-1-1111-11-1-1-1-11111-1-1-1-11111ii−i−i−i−iii-111-1-1-1-1111-1-111-1-1111111-1-1-1-11-1-11i−i−ii−i−iiiii−i−i-1-11111-1-1i−i−ii−iii−i
χ301-11-111-1-1-1-1-1111-11-1-1-1-11111-1-1-1-11111ii−i−i−i−iii-1-1-11111-1-11-1-111-1-1111111-1-1-1-1-111-1i−i−ii−i−iiiii−i−i11-1-1-1-111−iii−ii−i−ii
χ311-11-111-1-1-1-1-1111-11-1-1-1-11111-1-1-1-11111−i−iiiii−i−i-111-1-1-1-1111-1-111-1-1111111-1-1-1-11-1-11−iii−iii−i−i−i−iii-1-11111-1-1−iii−ii−i−ii
χ321-11-111-1-1-1-1-1111-11-1-1-1-11111-1-1-1-11111−i−iiiii−i−i-1-1-11111-1-11-1-111-1-1111111-1-1-1-1-111-1−iii−iii−i−i−i−iii11-1-1-1-111i−i−ii−iii−i
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χ4022222222-2-22-2222-200000000-2-2-2-2-2-2-2-200000000-2-2-2-2-22222-2222200000000000022-2-20000000000000000000000000000
χ412222-2-2-2-22-202000-222-2-222-2-222−2−222−2−22-22-22-22-200000000002−22−2000022−2−222−2−2000000002−22−22−22−20000000000000000
χ422222-2-2-2-22-202000-222-2-222-2-222−2−222−2−2-22-22-22-2200000000002−22−2000022−2−222−2−200000000−22−22−22−220000000000000000
χ432222-2-2-2-22-202000-222-2-222-2-2−2−222−2−2222-22-22-22-20000000000−22−220000−2−222−2−22200000000−22−22−22−220000000000000000
χ442222-2-2-2-22-202000-222-2-222-2-2−2−222−2−222-22-22-22-220000000000−22−220000−2−222−2−222000000002−22−22−22−20000000000000000
χ452222-2-2-2-22-202000-2-2-222-2-22222−2−222−2−22-22-2-22-2200000000002−22−20000−2−222−2−222000000002−22−2−22−220000000000000000
χ462222-2-2-2-22-202000-2-2-222-2-22222−2−222−2−2-22-222-22-200000000002−22−20000−2−222−2−22200000000−22−222−22−20000000000000000
χ472222-2-2-2-22-202000-2-2-222-2-222−2−222−2−2222-22-2-22-220000000000−22−22000022−2−222−2−200000000−22−222−22−20000000000000000
χ482222-2-2-2-22-202000-2-2-222-2-222−2−222−2−222-22-222-22-20000000000−22−22000022−2−222−2−2000000002−22−2−22−220000000000000000
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χ572-22-222-2-222-2-222-2-2000000002222-2-2-2-200000000222-2-222-2-2-2-2-222000000000000-22-220000000000000000000000000000
χ582-22-222-2-222-2-222-2-2000000002222-2-2-2-2000000002-2-222-2-222-2-2-2220000000000002-22-20000000000000000000000000000
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χ944-4-444-4-4400-40-4440−2222−222222−2222−2200000000000000000000000000000022−22−22220000000000000000000000000000000000000000
χ954-4-44-444-40000000022−22−2222−222222−222i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ964-4-44-444-40000000022−22−2222−222222−22−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ974-4-44-444-400000000−222222−2222−22−22222i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ984-4-44-444-400000000−222222−2222−22−2222−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000

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