Finite Group Databasebeta

← Group #231568

Character table — Group #231568

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888844444444888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11-1-1-1-11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ171-1-1111-1-1-11111-1-1-11111-1-1-1-11111-1-1-1-1ii−i−i-1ii−i−iii−i−iii−i−i111-1-111-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ181-1-1111-1-1-11111-1-1-11111-1-1-1-11111-1-1-1-1ii−i−i-1ii−i−i−i−iii−i−iii111-1-111-1-11111-1-1-1-1i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii-11-11-11-11
χ191-1-1111-1-1-11111-1-1-11111-1-1-1-11111-1-1-1-1−i−iii-1−i−iiiii−i−iii−i−i111-1-111-1-11111-1-1-1-1−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i-11-11-11-11
χ201-1-1111-1-1-11111-1-1-11111-1-1-1-11111-1-1-1-1−i−iii-1−i−iii−i−iii−i−iii111-1-111-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ211-1-1111-1-1-11111-1-1-11111-1-1-1-1-1-1-1-11111ii−i−i-1ii−i−iii−i−i−i−iii111-1-1-1-111-1-1-1-11111i−ii−ii−i−ii−i−iii−i−iiiii−i−i−i−iii1-11-1-11-11
χ221-1-1111-1-1-11111-1-1-11111-1-1-1-1-1-1-1-11111ii−i−i-1ii−i−i−i−iiiii−i−i111-1-1-1-111-1-1-1-11111i−ii−i−iii−i−i−iii−i−iii−i−iiiii−i−i-11-111-11-1
χ231-1-1111-1-1-11111-1-1-11111-1-1-1-1-1-1-1-11111−i−iii-1−i−iiiii−i−i−i−iii111-1-1-1-111-1-1-1-11111−ii−iii−i−iiii−i−iii−i−iii−i−i−i−iii-11-111-11-1
χ241-1-1111-1-1-11111-1-1-11111-1-1-1-1-1-1-1-11111−i−iii-1−i−iii−i−iiiii−i−i111-1-1-1-111-1-1-1-11111−ii−ii−iii−iii−i−iii−i−i−i−iiiii−i−i1-11-1-11-11
χ251-1-1111-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i-1−i−iiiii−i−iii−i−i1-1-11111-1-1-1-1-1-11111−iii−ii−ii−iii−i−i−i−iii−i−iii−i−iii-111-11-1-11
χ261-1-1111-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i-1−i−iii−i−iii−i−iii1-1-11111-1-1-1-1-1-11111−iii−i−ii−iiii−i−i−i−iiiii−i−iii−i−i1-1-11-111-1
χ271-1-1111-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-1−i−iii-1ii−i−iii−i−iii−i−i1-1-11111-1-1-1-1-1-11111i−i−iii−ii−i−i−iiiii−i−i−i−iii−i−iii1-1-11-111-1
χ281-1-1111-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-1−i−iii-1ii−i−i−i−iii−i−iii1-1-11111-1-1-1-1-1-11111i−i−ii−ii−ii−i−iiiii−i−iii−i−iii−i−i-111-11-1-11
χ291-1-1111-1-1-11111-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i-1−i−iiiii−i−i−i−iii1-1-111-1-1111111-1-1-1-1−iii−ii−i−ii−i−iiiii−i−i−i−iiiii−i−i-111-1-111-1
χ301-1-1111-1-1-11111-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i-1−i−iii−i−iiiii−i−i1-1-111-1-1111111-1-1-1-1−iii−i−iii−i−i−iiiii−i−iii−i−i−i−iii1-1-111-1-11
χ311-1-1111-1-1-11111-1-1-1-1-1-1-11111-1-1-1-11111−i−iii-1ii−i−iii−i−i−i−iii1-1-111-1-1111111-1-1-1-1i−i−iii−i−iiii−i−i−i−iii−i−iiiii−i−i1-1-111-1-11
χ321-1-1111-1-1-11111-1-1-1-1-1-1-11111-1-1-1-11111−i−iii-1ii−i−i−i−iiiii−i−i1-1-111-1-1111111-1-1-1-1i−i−ii−iii−iii−i−i−i−iiiii−i−i−i−iii-111-1-111-1
χ3322222222222-2-2-2-2222222222000000002222-2222200000000-2-2-2-2-2000000000000-2-2-2-20000000000000000000000000000
χ3422222222222-2-2-2-222222222200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-2-200000000000022220000000000000000000000000000
χ3522222222222-2-2-2-22-2-2-2-2-2-2-2-2000000002222-2-2-2-2-200000000-2222200000000000022-2-20000000000000000000000000000
χ3622222222222-2-2-2-22-2-2-2-2-2-2-2-200000000-2-2-2-2-2222200000000-22222000000000000-2-2220000000000000000000000000000
χ3722222222-2-2-22222-200000000222222220000-2000022222222-20000-2-2-2-2000000000000-2-2-2-2000000000000000000000000
χ3822222222-2-2-22222-200000000222222220000-20000-2-2-2-2-2-2-2-2-20000-2-2-2-20000000000002222000000000000000000000000
χ3922222222-2-2-22222-200000000-2-2-2-2-2-2-2-20000-200002222-2-2-2-2-200002222000000000000-2-222000000000000000000000000
χ4022222222-2-2-22222-200000000-2-2-2-2-2-2-2-20000-20000-2-2-2-22222-20000222200000000000022-2-2000000000000000000000000
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χ422222-2-2-2-2-22-2000022i2i−2i−2i2i2i−2i−2i22−2−222−2−2-22-220−2i2i−2i2i00000000000002−22−2i2i2−i2−i2i2i2−i2−i200000000−22−22−i2i2−i2i20000000000000000
χ432222-2-2-2-2-22-2000022i2i−2i−2i2i2i−2i−2i−2−222−2−2222-22-202i−2i2i−2i0000000000000−22−22−i2−i2i2i2−i2−i2i2i200000000−22−22−i2i2−i2i20000000000000000
χ442222-2-2-2-2-22-2000022i2i−2i−2i2i2i−2i−2i−2−222−2−222-22-220−2i2i−2i2i0000000000000−22−22−i2−i2i2i2−i2−i2i2i2000000002−22−2i2−i2i2−i20000000000000000
χ452222-2-2-2-2-22-200002−2i−2i2i2i−2i−2i2i2i22−2−222−2−22-22-20−2i2i−2i2i00000000000002−22−2−i2−i2i2i2−i2−i2i2i2000000002−22−2−i2i2−i2i20000000000000000
χ462222-2-2-2-2-22-200002−2i−2i2i2i−2i−2i2i2i22−2−222−2−2-22-2202i−2i2i−2i00000000000002−22−2−i2−i2i2i2−i2−i2i2i200000000−22−22i2−i2i2−i20000000000000000
χ472222-2-2-2-2-22-200002−2i−2i2i2i−2i−2i2i2i−2−222−2−2222-22-20−2i2i−2i2i0000000000000−22−22i2i2−i2−i2i2i2−i2−i200000000−22−22i2−i2i2−i20000000000000000
χ482222-2-2-2-2-22-200002−2i−2i2i2i−2i−2i2i2i−2−222−2−222-22-2202i−2i2i−2i0000000000000−22−22i2i2−i2−i2i2i2−i2−i2000000002−22−2−i2i2−i2i20000000000000000
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χ702-2-2222-2-2-222-2-222-22222-2-2-2-200000000−2i−2i2i2i2−2i−2i2i2i00000000-2-2-2220000000000002i−2i2i−2i0000000000000000000000000000
χ712-2-2222-2-2-222-2-222-2-2-2-2-22222000000002i2i−2i−2i2−2i−2i2i2i00000000-222-2-20000000000002i−2i−2i2i0000000000000000000000000000
χ722-2-2222-2-2-222-2-222-2-2-2-2-2222200000000−2i−2i2i2i22i2i−2i−2i00000000-222-2-2000000000000−2i2i2i−2i0000000000000000000000000000
χ732-2-22-2-22222-20000-22i2i−2i−2i−2i−2i2i2i22−2−2−2−2222i−2i−2i2i0-222-200000000000002−2−22i2i2−i2−i2−i2−i2i2i200000000i2−i2−i2i2−222−20000000000000000
χ742-2-22-2-22222-20000-22i2i−2i−2i−2i−2i2i2i22−2−2−2−222−2i2i2i−2i02-2-2200000000000002−2−22i2i2−i2−i2−i2−i2i2i200000000−i2i2i2−i22−2−220000000000000000
χ752-2-22-2-22222-20000-22i2i−2i−2i−2i−2i2i2i−2−22222−2−22i−2i−2i2i0-222-20000000000000−222−2−i2−i2i2i2i2i2−i2−i200000000−i2i2i2−i22−2−220000000000000000
χ762-2-22-2-22222-20000-22i2i−2i−2i−2i−2i2i2i−2−22222−2−2−2i2i2i−2i02-2-220000000000000−222−2−i2−i2i2i2i2i2−i2−i200000000i2−i2−i2i2−222−20000000000000000
χ772-2-22-2-22222-20000-2−2i−2i2i2i2i2i−2i−2i22−2−2−2−2222i−2i−2i2i02-2-2200000000000002−2−22−i2−i2i2i2i2i2−i2−i200000000i2−i2−i2i22−2−220000000000000000
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χ834444-4-4-4-44-440000-400000000−22−222222−22−222222000000000000000000000022−2222−220000000000000000000000000000000000000000
χ8444-4-44-44-4000-44-4402i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ8544-4-44-44-4000-44-440−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ8644-4-4-44-440000000022−22−222222−22−22222i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ8744-4-4-44-440000000022−22−222222−22−2222−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ8844-4-4-44-4400000000−222222−22−222222−222i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ8944-4-4-44-4400000000−222222−22−222222−22−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ904-44-44-4-44000-444-402i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ914-44-44-4-44000-444-40−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ924-44-4-444-40000000022−22−2222−222222−222i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ934-44-4-444-40000000022−22−2222−222222−22−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ944-44-4-444-400000000−222222−2222−22−22222i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ954-44-4-444-400000000−222222−2222−22−2222−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ964-4-4444-4-44-4-4-4-444400000000000000000000-40000000000004000000000000000000000000000000000000000000000000
χ974-4-44-4-444-4-4400004000000002222−22−22−22−2222220000000000000000000000−222222−220000000000000000000000000000000000000000
χ984-4-44-4-444-4-440000400000000−22−2222222222−22−22000000000000000000000022−22−22220000000000000000000000000000000000000000

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