Finite Group Databasebeta

← Group #160713

Character table — Group #160713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222444444444444444444444444444444442244444444444444224444444444444488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i
χ101111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ1711111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ1811111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ1911111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-111-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ2011111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-111-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ2111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii
χ2211111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i
χ2311111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i
χ2411111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-1
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1
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χ3822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-22222-2-2000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2222222-2-2000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-222-2-22222-2-2-2-2-2-222000000000000000000000000000000000000000000000000
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χ462222-2-2-2-22222-2-2-2-20000−2i−2i2i2i22-2-222-2-20000−2i−2i2i2i0000000000−2i2i00−2i2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
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χ492222-2-2-2-2-2-2-2-2222200002i2i−2i−2i22-2-2-2-2220000−2i−2i2i2i00000000002i−2i00−2i2i00000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ502222-2-2-2-2-2-2-2-2222200002i2i−2i−2i22-2-2-2-2220000−2i−2i2i2i00000000002i−2i00−2i2i0000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
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χ6222-2-222-2-22i2i−2i−2i2i2i−2i−2i-2-2222-22-200000000−2i−2i2i2i2i−2i2i−2i00-22−2i2i0000000000-22−2i2i2-22i−2i0000000000000000000000000000000000000000
χ6322-2-222-2-22i2i−2i−2i2i2i−2i−2i-2-222-22-2200000000−2i−2i2i2i−2i2i−2i2i002-22i−2i0000000000000000002-22i−2i-22−2i2i00000000000000000000000000000000
χ6422-2-222-2-22i2i−2i−2i2i2i−2i−2i-2-222-22-2200000000−2i−2i2i2i−2i2i−2i2i002-22i−2i000000000000000000-22−2i2i2-22i−2i00000000000000000000000000000000
χ6522-2-222-2-2−2i−2i2i2i−2i−2i2i2i22-2-22-22-200000000−2i−2i2i2i−2i2i−2i2i002-2−2i2i0000000000000000002-2−2i2i2-2−2i2i00000000000000000000000000000000
χ6622-2-222-2-2−2i−2i2i2i−2i−2i2i2i22-2-22-22-200000000−2i−2i2i2i−2i2i−2i2i002-2−2i2i000000000000000000-222i−2i-222i−2i00000000000000000000000000000000
χ6722-2-222-2-2−2i−2i2i2i−2i−2i2i2i22-2-2-22-2200000000−2i−2i2i2i2i−2i2i−2i00-222i−2i00000000002-2−2i2i2-2−2i2i0000000000000000000000000000000000000000
χ6822-2-222-2-2−2i−2i2i2i−2i−2i2i2i22-2-2-22-2200000000−2i−2i2i2i2i−2i2i−2i00-222i−2i0000000000-222i−2i-222i−2i0000000000000000000000000000000000000000
χ6922-2-222-2-2−2i−2i2i2i−2i−2i2i2i-2-2222-22-2000000002i2i−2i−2i−2i2i−2i2i00-222i−2i00000000002-2−2i2i-222i−2i0000000000000000000000000000000000000000
χ7022-2-222-2-2−2i−2i2i2i−2i−2i2i2i-2-2222-22-2000000002i2i−2i−2i−2i2i−2i2i00-222i−2i0000000000-222i−2i2-2−2i2i0000000000000000000000000000000000000000
χ7122-2-222-2-2−2i−2i2i2i−2i−2i2i2i-2-222-22-22000000002i2i−2i−2i2i−2i2i−2i002-2−2i2i0000000000000000002-2−2i2i-222i−2i00000000000000000000000000000000
χ7222-2-222-2-2−2i−2i2i2i−2i−2i2i2i-2-222-22-22000000002i2i−2i−2i2i−2i2i−2i002-2−2i2i000000000000000000-222i−2i2-2−2i2i00000000000000000000000000000000
χ732-22-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00002i−2i2i−2i2-22-22-22-200002-200000000002i−2i00000000000000000000000000000000002−2i2−i2i2−i22−2i2−i22−22−2i2−i2
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χ762-22-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000−2i2i−2i2i-22-222-22-20000-220000000000−2i2i0000000000000000000000000000000000−22−i2i2−i2i2−22i2−i22−22−2i2−i2
χ772-22-22-22-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i00002i−2i2i−2i2-22-2-22-220000-220000000000−2i2i0000000000000000000000000000000000i2−i2−222−2−i2i2−22i2−i2−i2i22−2
χ782-22-22-22-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i00002i−2i2i−2i2-22-2-22-220000-220000000000−2i2i0000000000000000000000000000000000−i2i22−2−22i2−i22−2−i2i2i2−i2−22
χ792-22-22-22-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i0000−2i2i−2i2i-22-22-22-2200002-200000000002i−2i0000000000000000000000000000000000i2−i2−222−2−i2i22−2−i2i2i2−i2−22
χ802-22-22-22-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i0000−2i2i−2i2i-22-22-22-2200002-200000000002i−2i0000000000000000000000000000000000−i2i22−2−22i2−i2−22i2−i2−i2i22−2
χ812-22-22-22-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00002i−2i2i−2i-22-22-22-2200002-20000000000−2i2i0000000000000000000000000000000000i2−i22−2−22−i2i2−22−i2i2i2−i22−2
χ822-22-22-22-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00002i−2i2i−2i-22-22-22-2200002-20000000000−2i2i0000000000000000000000000000000000−i2i2−222−2i2−i22−2i2−i2−i2i2−22
χ832-22-22-22-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i0000−2i2i−2i2i2-22-2-22-220000-2200000000002i−2i0000000000000000000000000000000000i2−i22−2−22−i2i22−2i2−i2−i2i2−22
χ842-22-22-22-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i0000−2i2i−2i2i2-22-2-22-220000-2200000000002i−2i0000000000000000000000000000000000−i2i2−222−2i2−i2−22−i2i2i2−i22−2
χ852-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00002i−2i2i−2i-22-222-22-20000-2200000000002i−2i00000000000000000000000000000000002−2−i2i2−i2i22−2i2−i2−22−22i2−i2
χ862-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00002i−2i2i−2i-22-222-22-20000-2200000000002i−2i0000000000000000000000000000000000−22i2−i2i2−i2−22−i2i22−22−2−i2i2
χ872-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000−2i2i−2i2i2-22-22-22-200002-20000000000−2i2i00000000000000000000000000000000002−2−i2i2−i2i22−2−i2i22−22−2−i2i2
χ882-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000−2i2i−2i2i2-22-22-22-200002-20000000000−2i2i0000000000000000000000000000000000−22i2−i2i2−i2−22i2−i2−22−22i2−i2
χ8944-4-4-4-4444i4i−4i−4i−4i−4i4i4i00004i−4i−4i4i000000000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ9044-4-4-4-4444i4i−4i−4i−4i−4i4i4i0000−4i4i4i−4i0000000000004-4-440000000000000000000000000000000000000000000000000000000000000000
χ9144-4-4-4-444−4i−4i4i4i4i4i−4i−4i00004i−4i−4i4i0000000000004-4-440000000000000000000000000000000000000000000000000000000000000000
χ9244-4-4-4-444−4i−4i4i4i4i4i−4i−4i0000−4i4i4i−4i000000000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ934-44-4-44-444i−4i4i−4i−4i4i−4i4i000000004i−4i−4i4i4-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ944-44-4-44-444i−4i4i−4i−4i4i−4i4i00000000−4i4i4i−4i-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ954-44-4-44-44−4i4i−4i4i4i−4i4i−4i000000004i−4i−4i4i-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ964-44-4-44-44−4i4i−4i4i4i−4i4i−4i00000000−4i4i4i−4i4-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ974-4-444-4-444-4-444-4-444i−4i−4i4i000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ984-4-444-4-444-4-444-4-44−4i4i4i−4i0000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ994-4-444-4-44-444-4-444-44i−4i−4i4i0000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ1004-4-444-4-44-444-4-444-4−4i4i4i−4i000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-44-444-44-4-44-444-40000000000000000000000000000004i−4i4i−4i000000000000000000000000000000000000000000000000000000
χ1024-4-44-444-44-4-44-444-4000000000000000000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000000000
χ1034-4-44-444-4-444-44-4-440000000000000000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ1044-4-44-444-4-444-44-4-44000000000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000

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