Finite Group Databasebeta

← Group #229265

Character table — Group #229265

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888822444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ121111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1711-11-1-1-11-111-1-1-111iiii−i−i−i−i1111-1-1-1-1111-1-1ii−i−iii−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
χ1811-11-1-1-11-111-1-1-111iiii−i−i−i−i1111-1-1-1-1111-1-1−i−iii−i−iiiii−i−i-1ii−i−i11-1-1iiii−i−i−i−i1-1i−i−ii−iiii−i−i11-1-1-1-111-1-111−ii−ii-11-11
χ1911-11-1-1-11-111-1-1-111iiii−i−i−i−i1111-1-1-1-11-1-111ii−i−iii−i−i−i−iii-1ii−i−i11-1-1iiii−i−i−i−i-11−iii−ii−i−i−iii-1-11111-1-111-1-1−ii−ii-11-11
χ2011-11-1-1-11-111-1-1-111iiii−i−i−i−i1111-1-1-1-11-1-111−i−iii−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
χ2111-11-1-1-11-111-1-1-111iiii−i−i−i−i-1-1-1-11111111-1-1ii−i−i−i−iiiii−i−i-1ii−i−i-1-111−i−i−i−iiiii1-1i−ii−i−ii−i−iii-1-11111-1-1-1-111i−i−ii1-1-11
χ2211-11-1-1-11-111-1-1-111iiii−i−i−i−i-1-1-1-11111111-1-1−i−iiiii−i−iii−i−i-1ii−i−i-1-111−i−i−i−iiiii1-1i−i−iii−i−i−iii-1-111-1-11111-1-1−iii−i-111-1
χ2311-11-1-1-11-111-1-1-111iiii−i−i−i−i-1-1-1-111111-1-111ii−i−i−i−iii−i−iii-1ii−i−i-1-111−i−i−i−iiiii-11−iii−i−iiii−i−i11-1-111-1-1-1-111−iii−i-111-1
χ2411-11-1-1-11-111-1-1-111iiii−i−i−i−i-1-1-1-111111-1-111−i−iiiii−i−i−i−iii-1ii−i−i-1-111−i−i−i−iiiii-11−ii−iii−iii−i−i11-1-1-1-11111-1-1i−i−ii1-1-11
χ2511-11-1-1-11-111-1-1-111−i−i−i−iiiii1111-1-1-1-1111-1-1ii−i−iii−i−i−i−iii-1−i−iii11-1-1−i−i−i−iiiii1-1−iii−ii−i−i−iii11-1-1-1-111-1-111i−ii−i-11-11
χ2611-11-1-1-11-111-1-1-111−i−i−i−iiiii1111-1-1-1-1111-1-1−i−iii−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
χ2711-11-1-1-11-111-1-1-111−i−i−i−iiiii1111-1-1-1-11-1-111ii−i−iii−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
χ2811-11-1-1-11-111-1-1-111−i−i−i−iiiii1111-1-1-1-11-1-111−i−iii−i−iiiii−i−i-1−i−iii11-1-1−i−i−i−iiiii-11i−i−ii−iiii−i−i-1-11111-1-111-1-1i−ii−i-11-11
χ2911-11-1-1-11-111-1-1-111−i−i−i−iiiii-1-1-1-11111111-1-1ii−i−i−i−iii−i−iii-1−i−iii-1-111iiii−i−i−i−i1-1−iii−i−iiii−i−i-1-111-1-11111-1-1i−i−ii-111-1
χ3011-11-1-1-11-111-1-1-111−i−i−i−iiiii-1-1-1-11111111-1-1−i−iiiii−i−i−i−iii-1−i−iii-1-111iiii−i−i−i−i1-1−ii−iii−iii−i−i-1-11111-1-1-1-111−iii−i1-1-11
χ3111-11-1-1-11-111-1-1-111−i−i−i−iiiii-1-1-1-111111-1-111ii−i−i−i−iiiii−i−i-1−i−iii-1-111iiii−i−i−i−i-11i−ii−i−ii−i−iii11-1-1-1-11111-1-1−iii−i1-1-11
χ3211-11-1-1-11-111-1-1-111−i−i−i−iiiii-1-1-1-111111-1-111−i−iiiii−i−iii−i−i-1−i−iii-1-111iiii−i−i−i−i-11i−i−iii−i−i−iii11-1-111-1-1-1-111i−i−ii-111-1
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χ34222222222-22-2-222-20000000022222222-20000-2-2-2-2-2-2-2-20000-20000-2-2-2-20000000000002222000000000000000000000000
χ35222222222-22-2-222-200000000-2-2-2-2-2-2-2-2-200002222-2-2-2-20000-200002222000000000000-2-222000000000000000000000000
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χ3722222222-22-222-2-222222222200000000-22222000000002222-2-2-2-2-2000000000000-2-2-2-20000000000000000000000000000
χ3822222222-22-222-2-222222222200000000-2-2-2-2-200000000-2-2-2-2-2-2-2-2-200000000000022220000000000000000000000000000
χ3922222222-22-222-2-22-2-2-2-2-2-2-2-200000000-2222200000000-2-2-2-2-22222000000000000-2-2220000000000000000000000000000
χ4022222222-22-222-2-22-2-2-2-2-2-2-2-200000000-2-2-2-2-2000000002222-2222200000000000022-2-20000000000000000000000000000
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χ4222-22-2-2-2222-2-2-22-222i2i2i2i−2i−2i−2i−2i00000000-2-2-22200000000−2i−2i2i2i2−2i−2i2i2i0000000000002-22i−2i0000000000000000000000000000
χ4322-22-2-2-2222-2-2-22-22−2i−2i−2i−2i2i2i2i2i00000000-222-2-200000000−2i−2i2i2i22i2i−2i−2i000000000000-222i−2i0000000000000000000000000000
χ4422-22-2-2-2222-2-2-22-22−2i−2i−2i−2i2i2i2i2i00000000-2-2-222000000002i2i−2i−2i22i2i−2i−2i0000000000002-2−2i2i0000000000000000000000000000
χ4522-22-2-2-22-2-2222-22-2000000002222-2-2-2-2-200002i2i−2i−2i2i2i−2i−2i000020000-2-222000000000000−2i2i−2i2i000000000000000000000000
χ4622-22-2-2-22-2-2222-22-2000000002222-2-2-2-2-20000−2i−2i2i2i−2i−2i2i2i000020000-2-2220000000000002i−2i2i−2i000000000000000000000000
χ4722-22-2-2-22-2-2222-22-200000000-2-2-2-22222-200002i2i−2i−2i−2i−2i2i2i00002000022-2-2000000000000−2i2i2i−2i000000000000000000000000
χ4822-22-2-2-22-2-2222-22-200000000-2-2-2-22222-20000−2i−2i2i2i2i2i−2i−2i00002000022-2-20000000000002i−2i−2i2i000000000000000000000000
χ492-222-22-2-2-20-20022022−2−222−2−222-2-222-2-2000002i−2i2i−2i2i−2i2i−2i000002−22−2000022−2−222−2−20000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ502-222-22-2-2-20-20022022−2−222−2−222-2-222-2-200000−2i2i−2i2i−2i2i−2i2i000002−22−2000022−2−222−2−20000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ512-222-22-2-2-20-20022022−2−222−2−2-2-222-2-222000002i−2i2i−2i−2i2i−2i2i000002−22−20000−2−222−2−2220000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ522-222-22-2-2-20-20022022−2−222−2−2-2-222-2-22200000−2i2i−2i2i2i−2i2i−2i000002−22−20000−2−222−2−2220000000000000000−i2i2−i2i2i2−i2i2−i200000000
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χ542-222-22-2-2-20-200220−2−222−2−22222-2-222-2-200000−2i2i−2i2i−2i2i−2i2i00000−22−220000−2−222−2−2220000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ552-222-22-2-2-20-200220−2−222−2−222-2-222-2-222000002i−2i2i−2i−2i2i−2i2i00000−22−22000022−2−222−2−20000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ562-222-22-2-2-20-200220−2−222−2−222-2-222-2-22200000−2i2i−2i2i2i−2i2i−2i00000−22−22000022−2−222−2−20000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ572-22-2-2-2220202-200-22-22-22-22-22−22−22−22−202i−2i2i−2i000000002i−2i2i−2i000002−22−22−22−22−22−200000000i2−i2i2−i2i2−i2i2−i20000000000000000
χ582-22-2-2-2220202-200-22-22-22-22-22−22−22−22−20−2i2i−2i2i00000000−2i2i−2i2i000002−22−22−22−22−22−200000000−i2i2−i2i2−i2i2−i2i20000000000000000
χ592-22-2-2-2220202-200-22-22-22-22-2−22−22−22−2202i−2i2i−2i000000002i−2i2i−2i00000−22−22−22−22−22−2200000000−i2i2−i2i2−i2i2−i2i20000000000000000
χ602-22-2-2-2220202-200-22-22-22-22-2−22−22−22−220−2i2i−2i2i00000000−2i2i−2i2i00000−22−22−22−22−22−2200000000i2−i2i2−i2i2−i2i2−i20000000000000000
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χ622-22-2-2-2220202-200-2-22-22-22-222−22−22−22−20−2i2i−2i2i000000002i−2i2i−2i000002−22−2−22−22−22−2200000000i2−i2i2−i2−i2i2−i2i20000000000000000
χ632-22-2-2-2220202-200-2-22-22-22-22−22−22−22−2202i−2i2i−2i00000000−2i2i−2i2i00000−22−222−22−22−22−200000000i2−i2i2−i2−i2i2−i2i20000000000000000
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χ672-2-222-22-220-200-220i2i2−i2−i2−i2−i2i2i2-2-22222-2-2000002-2-22-222-200000i2−i2−i2i20000−i2−i2i2i2i2i2−i2−i20000000000000000−i2i2i2−i2i2−i2−i2i200000000
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χ712-2-222-22-220-200-220−i2−i2i2i2i2i2−i2−i2-2-22222-2-2000002-2-22-222-200000−i2i2i2−i20000i2i2−i2−i2−i2−i2i2i20000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ722-2-222-22-220-200-220−i2−i2i2i2i2i2−i2−i2-2-22222-2-200000-222-22-2-2200000−i2i2i2−i20000i2i2−i2−i2−i2−i2i2i20000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ732-2-2-222-22020-2200-22i−2i2i−2i−2i2i−2i2i2−22−2−22−2202i−2i−2i2i00000000-222-2000002−2−22i2−i2i2−i2−i2i2−i2i200000000−222−2i2−i2−i2i20000000000000000
χ742-2-2-222-22020-2200-22i−2i2i−2i−2i2i−2i2i2−22−2−22−220−2i2i2i−2i000000002-2-22000002−2−22i2−i2i2−i2−i2i2−i2i2000000002−2−22−i2i2i2−i20000000000000000
χ752-2-2-222-22020-2200-22i−2i2i−2i−2i2i−2i2i−22−222−22−202i−2i−2i2i00000000-222-200000−222−2−i2i2−i2i2i2−i2i2−i2000000002−2−22−i2i2i2−i20000000000000000
χ762-2-2-222-22020-2200-22i−2i2i−2i−2i2i−2i2i−22−222−22−20−2i2i2i−2i000000002-2-2200000−222−2−i2i2−i2i2i2−i2i2−i200000000−222−2i2−i2−i2i20000000000000000
χ772-2-2-222-22020-2200-2−2i2i−2i2i2i−2i2i−2i2−22−2−22−2202i−2i−2i2i000000002-2-22000002−2−22−i2i2−i2i2i2−i2i2−i2000000002−2−22i2−i2−i2i20000000000000000
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χ792-2-2-222-22020-2200-2−2i2i−2i2i2i−2i2i−2i−22−222−22−202i−2i−2i2i000000002-2-2200000−222−2i2−i2i2−i2−i2i2−i2i200000000−222−2−i2i2i2−i20000000000000000
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χ8744-4-4-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i222−22−2222−222222−22000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ8844-4-4-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i2−222222−2222−22−222200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ8944-4-4-444-400000000−2i22i22i2−2i22i2−2i2−2i22i222−22−2222−222222−2200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ9044-4-4-444-400000000−2i22i22i2−2i22i2−2i2−2i22i2−222222−2222−22−2222000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ914-444-44-4-440400-4-402222−22−222222−22−2200000000000000000000000000−2222−222200000000000000000000000000000000000000000000
χ924-444-44-4-440400-4-40−22−222222−22−2222220000000000000000000000000022−2222−2200000000000000000000000000000000000000000000
χ934-44-4-4-4440-40-440040000000022−2222−2222−2222−220000000000000000000000−2222−22220000000000000000000000000000000000000000
χ944-44-4-4-4440-40-4400400000000−2222−2222−2222−2222000000000000000000000022−2222−220000000000000000000000000000000000000000
χ954-4-444-44-4-404004-402i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ964-4-444-44-4-404004-40−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ974-4-4-444-440-404-40040000000022−2222−22−2222−22220000000000000000000000−222222−220000000000000000000000000000000000000000
χ984-4-4-444-440-404-400400000000−2222−222222−2222−22000000000000000000000022−22−22220000000000000000000000000000000000000000

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