Finite Group Databasebeta

← Group #229270

Character table — Group #229270

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888844444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11-1-1-1-11111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ101111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ171-111-1-1-111-1-1-11-111iiii−i−i−i−i1111-1-1-1-1ii−i−i111-1-1ii−i−iii−i−i-1ii−i−i11-1-1iiii−i−i−i−i1-1i−ii−ii−iii−i−i11-1-111-1-111-1-1i−ii−i1-11-1
χ181-111-1-1-111-1-1-11-111iiii−i−i−i−i1111-1-1-1-1ii−i−i111-1-1−i−iii−i−iii-1ii−i−i11-1-1iiii−i−i−i−i1-1−ii−iii−iii−i−i11-1-1-1-111-1-111−ii−ii-11-11
χ191-111-1-1-111-1-1-11-111iiii−i−i−i−i1111-1-1-1-1−i−iii1-1-111ii−i−iii−i−i-1ii−i−i11-1-1iiii−i−i−i−i-11i−ii−i−ii−i−iii-1-11111-1-111-1-1−ii−ii-11-11
χ201-111-1-1-111-1-1-11-111iiii−i−i−i−i1111-1-1-1-1−i−iii1-1-111−i−iii−i−iii-1ii−i−i11-1-1iiii−i−i−i−i-11−ii−ii−ii−i−iii-1-111-1-111-1-111i−ii−i1-11-1
χ211-111-1-1-111-1-1-11-111iiii−i−i−i−i-1-1-1-11111ii−i−i111-1-1ii−i−i−i−iii-1ii−i−i-1-111−i−i−i−iiiii1-1i−i−iii−i−i−iii-1-11111-1-1-1-111i−i−ii1-1-11
χ221-111-1-1-111-1-1-11-111iiii−i−i−i−i-1-1-1-11111ii−i−i111-1-1−i−iiiii−i−i-1ii−i−i-1-111−i−i−i−iiiii1-1−iii−ii−i−i−iii-1-111-1-11111-1-1−iii−i-111-1
χ231-111-1-1-111-1-1-11-111iiii−i−i−i−i-1-1-1-11111−i−iii1-1-111ii−i−i−i−iii-1ii−i−i-1-111−i−i−i−iiiii-11i−i−ii−iiii−i−i11-1-111-1-1-1-111−iii−i-111-1
χ241-111-1-1-111-1-1-11-111iiii−i−i−i−i-1-1-1-11111−i−iii1-1-111−i−iiiii−i−i-1ii−i−i-1-111−i−i−i−iiiii-11−iii−i−iiii−i−i11-1-1-1-11111-1-1i−i−ii1-1-11
χ251-111-1-1-111-1-1-11-111−i−i−i−iiiii1111-1-1-1-1ii−i−i1-1-111ii−i−iii−i−i-1−i−iii11-1-1−i−i−i−iiiii-11i−ii−ii−iii−i−i-1-111-1-111-1-111−ii−ii1-11-1
χ261-111-1-1-111-1-1-11-111−i−i−i−iiiii1111-1-1-1-1ii−i−i1-1-111−i−iii−i−iii-1−i−iii11-1-1−i−i−i−iiiii-11−ii−iii−iii−i−i-1-11111-1-111-1-1i−ii−i-11-11
χ271-111-1-1-111-1-1-11-111−i−i−i−iiiii1111-1-1-1-1−i−iii111-1-1ii−i−iii−i−i-1−i−iii11-1-1−i−i−i−iiiii1-1i−ii−i−ii−i−iii11-1-1-1-111-1-111i−ii−i-11-11
χ281-111-1-1-111-1-1-11-111−i−i−i−iiiii1111-1-1-1-1−i−iii111-1-1−i−iii−i−iii-1−i−iii11-1-1−i−i−i−iiiii1-1−ii−ii−ii−i−iii11-1-111-1-111-1-1−ii−ii1-11-1
χ291-111-1-1-111-1-1-11-111−i−i−i−iiiii-1-1-1-11111ii−i−i1-1-111ii−i−i−i−iii-1−i−iii-1-111iiii−i−i−i−i-11i−i−iii−i−i−iii11-1-1-1-11111-1-1−iii−i1-1-11
χ301-111-1-1-111-1-1-11-111−i−i−i−iiiii-1-1-1-11111ii−i−i1-1-111−i−iiiii−i−i-1−i−iii-1-111iiii−i−i−i−i-11−iii−ii−i−i−iii11-1-111-1-1-1-111i−i−ii-111-1
χ311-111-1-1-111-1-1-11-111−i−i−i−iiiii-1-1-1-11111−i−iii111-1-1ii−i−i−i−iii-1−i−iii-1-111iiii−i−i−i−i1-1i−i−ii−iiii−i−i-1-111-1-11111-1-1i−i−ii-111-1
χ321-111-1-1-111-1-1-11-111−i−i−i−iiiii-1-1-1-11111−i−iii111-1-1−i−iiiii−i−i-1−i−iii-1-111iiii−i−i−i−i1-1−iii−i−iiii−i−i-1-11111-1-1-1-111−iii−i1-1-11
χ33222222222-222-2-2-2222222222000000002222-2222200000000-2-2-2-2-2000000000000-2-20000-2-2000000000000000000000000
χ34222222222-222-2-2-222222222200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-2-200000000000022000022000000000000000000000000
χ35222222222-222-2-2-22-2-2-2-2-2-2-2-2000000002222-2-2-2-2-200000000-22222000000000000220000-2-2000000000000000000000000
χ36222222222-222-2-2-22-2-2-2-2-2-2-2-200000000-2-2-2-2-2222200000000-22222000000000000-2-2000022000000000000000000000000
χ3722222222-22-2-2222-200000000222222220000-2000022222222-20000-2-2-2-20000000000-2-2-2-200000000000000000000000000
χ3822222222-22-2-2222-200000000222222220000-20000-2-2-2-2-2-2-2-2-20000-2-2-2-20000000000222200000000000000000000000000
χ3922222222-22-2-2222-200000000-2-2-2-2-2-2-2-20000-200002222-2-2-2-2-2000022220000000000-2-22200000000000000000000000000
χ4022222222-22-2-2222-200000000-2-2-2-2-2-2-2-20000-20000-2-2-2-22222-200002222000000000022-2-200000000000000000000000000
χ41222-2-2-22-2-202-200022i2i−2i−2i2i2i−2i−2i22−2−222−2−22-22-202i−2i2i−2i00000000000002−22−2i2i2−i2−i2i2i2−i2−i2000000002−22−2i2−i2i2−i20000000000000000
χ42222-2-2-22-2-202-200022i2i−2i−2i2i2i−2i−2i22−2−222−2−2-22-220−2i2i−2i2i00000000000002−22−2i2i2−i2−i2i2i2−i2−i200000000−22−22−i2i2−i2i20000000000000000
χ43222-2-2-22-2-202-200022i2i−2i−2i2i2i−2i−2i−2−222−2−2222-22-202i−2i2i−2i0000000000000−22−22−i2−i2i2i2−i2−i2i2i200000000−22−22−i2i2−i2i20000000000000000
χ44222-2-2-22-2-202-200022i2i−2i−2i2i2i−2i−2i−2−222−2−222-22-220−2i2i−2i2i0000000000000−22−22−i2−i2i2i2−i2−i2i2i2000000002−22−2i2−i2i2−i20000000000000000
χ45222-2-2-22-2-202-20002−2i−2i2i2i−2i−2i2i2i22−2−222−2−22-22-20−2i2i−2i2i00000000000002−22−2−i2−i2i2i2−i2−i2i2i2000000002−22−2−i2i2−i2i20000000000000000
χ46222-2-2-22-2-202-20002−2i−2i2i2i−2i−2i2i2i22−2−222−2−2-22-2202i−2i2i−2i00000000000002−22−2−i2−i2i2i2−i2−i2i2i200000000−22−22i2−i2i2−i20000000000000000
χ47222-2-2-22-2-202-20002−2i−2i2i2i−2i−2i2i2i−2−222−2−2222-22-20−2i2i−2i2i0000000000000−22−22i2i2−i2−i2i2i2−i2−i200000000−22−22i2−i2i2−i20000000000000000
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χ4922-2-2-22-220-20022-20i2−i2i2−i2i2−i2i2−i22-22-22-22-20000000002-22-22-22-20i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i20000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ5022-2-2-22-220-20022-20i2−i2i2−i2i2−i2i2−i22-22-22-22-2000000000-22-22-22-220i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i20000000000000000−i2i2−i2i2−i2i2−i2i200000000
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χ5222-2-2-22-220-20022-20i2−i2i2−i2i2−i2i2−i2-22-22-22-22000000000-22-222-22-20i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i20000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ5322-2-2-22-220-20022-20−i2i2−i2i2−i2i2−i2i22-22-22-22-20000000002-22-22-22-20−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i20000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ5422-2-2-22-220-20022-20−i2i2−i2i2−i2i2−i2i22-22-22-22-2000000000-22-22-22-220−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i20000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ5522-2-2-22-220-20022-20−i2i2−i2i2−i2i2−i2i2-22-22-22-220000000002-22-2-22-220−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i20000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ5622-2-2-22-220-20022-20−i2i2−i2i2−i2i2−i2i2-22-22-22-22000000000-22-222-22-20−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i20000000000000000i2−i2i2−i2−i2i2−i2i200000000
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χ632-222-2-2-22-2-2222-22-200000000-2-2-2-222220000-200002i2i−2i−2i−2i−2i2i2i2000022-2-20000000000−2i2i2i−2i00000000000000000000000000
χ642-222-2-2-22-2-2222-22-200000000-2-2-2-222220000-20000−2i−2i2i2i2i2i−2i−2i2000022-2-200000000002i−2i−2i2i00000000000000000000000000
χ652-22-222-2-2-20-22000222-2-2-2-22222−2−2−2−2222i−2i−2i2i0−2i2i2i−2i00000000000002−2−2222−2−2−2−22200000000i2−i2−i2i2−i2i2i2−i20000000000000000
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χ8744-444-4-4-400000000−222222−22−222222−22−222222−22−222222−22000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ8844-4-4-44-440400-4-4402i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ8944-4-4-44-440400-4-440−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ904-444-4-4-44-4444-44-4-4000000000000000000004000000000000-4000000000000000000000000000000000000000000000000
χ914-44-444-4-4404-4000-4000000002222−22−22−22−2222220000000000000000000000−222222−220000000000000000000000000000000000000000
χ924-44-444-4-4404-4000-400000000−22−2222222222−22−22000000000000000000000022−22−22220000000000000000000000000000000000000000
χ934-4-44-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i222−22−2222−222222−22000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ944-4-44-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i2−222222−2222−22−222200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ954-4-44-444-400000000−2i22i22i2−2i22i2−2i2−2i22i222−22−2222−222222−2200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ964-4-44-444-400000000−2i22i22i2−2i22i2−2i2−2i22i2−222222−2222−22−2222000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ974-4-4-44-4440-400-444022−2222−22−2222−222200000000000000000000000000−222222−2200000000000000000000000000000000000000000000
χ984-4-4-44-4440-400-4440−2222−222222−2222−220000000000000000000000000022−22−222200000000000000000000000000000000000000000000

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