Finite Group Databasebeta

← Group #160921

Character table — Group #160921

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222444444444444444422444444444444244444444444444444448888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ7111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-111-1-11-1-1-1-1-111-1-111111ii−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-111-1-11-1-1-1-1-111-1-111111−i−iii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1111-11111-1-1111-1-1-1-1ii−i−i−i−i−i−iiiiiii−i−iiiii−i−i−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1111-11111-1-1111-1-1-1-1−i−iiiiiii−i−i−i−i−i−iii−i−i−i−iiiiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111-11-1-1-1-1-1-111-111-1-1ii−i−iiiii−i−i−i−iii−i−i−i−i−i−iiiii−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111-11-1-1-1-1-1-111-111-1-1−i−iii−i−i−i−iiiii−i−iiiiiii−i−i−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-11111111-1-1-1-1-111ii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-11111111-1-1-1-1-111−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iii
χ1711111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1111-1-11-111-1-11111-1-1-1-1-1ii−i−iii−i−iii−i−i−i−iiiii−i−iii−i−ii−ii−i
χ1811111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1111-1-11-111-1-11111-1-1-1-1-1−i−iii−i−iii−i−iiiii−i−i−i−iii−i−iii−ii−ii
χ1911111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-11-1-1111-1-1-111-1-1-1-1-11111ii−i−i−i−iii−i−iii−i−iiiii−i−iii−i−i−ii−ii
χ2011111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-11-1-1111-1-1-111-1-1-1-1-11111−i−iiiii−i−iii−i−iii−i−i−i−iii−i−iiii−ii−i
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-11111-1111-1-1-1-1-1-11-1-111ii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−ii−ii
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-11111-1111-1-1-1-1-1-11-1-111−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−ii−ii−i
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11-1-1111111111-1-1ii−i−i−i−iii−i−iii−i−iii−i−iii−i−iiii−ii−i
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11-1-1111111111-1-1−i−iiiii−i−iii−i−iii−i−iii−i−iii−i−i−ii−ii
χ2511111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-1111111-1-11111-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1111-1-11
χ2611111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-111-1
χ2711111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-111-111111111-1-11111-1-1-1-1-1-111-1-1-1-111-111-1
χ2811111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-111-11111-1-1-1-111-1-1-1-1111111-1-11111-1-11-1-11
χ2911111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1111-1-1-1-1-1-111-1-1111-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-111-1
χ3011111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1111-1-1-1-1-1-111-1-1111-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-1111-1-11
χ3111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-11-1-111-1-111-1-111-1-1111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-11-1-11
χ3211111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-11-1-111-1-111-1-111-1-1111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-111-1
χ332222222222222222-2-22222-2-222-2-2-2-2-2-2222222-20000-2-200000000-200000000000000000000000000000000
χ342222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2200002200000000200000000000000000000000000000000
χ35222222222222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-220000-2200000000-200000000000000000000000000000000
χ36222222222222-2-2-2-222-2-2-2-222-2-2-2-2-2-222-2-22222-200002-200000000200000000000000000000000000000000
χ3722222222-2-2-2-2222222-2-2-2-2222222-2-2-2-2-2-222-2-2-20000-2200000000200000000000000000000000000000000
χ3822222222-2-2-2-2222222-2-2-2-222-2-222-2-2-2-222-2-222200002-200000000-200000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-22222-2-22222-2-222-2-2-2-22220000-2-200000000200000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222-2-2222222-2-2-200002200000000-200000000000000000000000000000000
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χ422-22-222-2-222-2-22i2i−2i−2i002i2i−2i−2i002-20000002-22i−2i2i−2i00000000000000000000−1−i1+i−1+i1−i00000000−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ432-22-222-2-222-2-22i2i−2i−2i002i2i−2i−2i00-22000000-22−2i2i−2i2i000000000000000000001+i−1−i1−i−1+i000000001+i−1−i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ442-22-222-2-222-2-22i2i−2i−2i002i2i−2i−2i00-22000000-22−2i2i−2i2i00000000000000000000−1−i1+i−1+i1−i00000000−1−i1+i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ452-22-222-2-222-2-2−2i−2i2i2i00−2i−2i2i2i002-20000002-2−2i2i−2i2i000000000000000000001−i−1+i1+i−1−i000000001−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
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χ472-22-222-2-222-2-2−2i−2i2i2i00−2i−2i2i2i00-22000000-222i−2i2i−2i000000000000000000001−i−1+i1+i−1−i000000001−i−1+i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ482-22-222-2-222-2-2−2i−2i2i2i00−2i−2i2i2i00-22000000-222i−2i2i−2i00000000000000000000−1+i1−i−1−i1+i00000000−1+i1−i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ492-22-222-2-2-2-2222i2i−2i−2i00−2i−2i2i2i002-2000000-222i−2i−2i2i000000000000000000001−i−1+i1+i−1−i00000000−1+i1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
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χ522-22-222-2-2-2-2222i2i−2i−2i00−2i−2i2i2i00-220000002-2−2i2i2i−2i00000000000000000000−1+i1−i−1−i1+i000000001−i−1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ532-22-222-2-2-2-222−2i−2i2i2i002i2i−2i−2i002-2000000-22−2i2i2i−2i000000000000000000001+i−1−i1−i−1+i00000000−1−i1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ542-22-222-2-2-2-222−2i−2i2i2i002i2i−2i−2i002-2000000-22−2i2i2i−2i00000000000000000000−1−i1+i−1+i1−i000000001+i−1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ552-22-222-2-2-2-222−2i−2i2i2i002i2i−2i−2i00-220000002-22i−2i−2i2i000000000000000000001+i−1−i1−i−1+i00000000−1−i1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
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χ572-2-222-22-22i−2i2i−2i2-22-22i−2i2i−2i2i−2i2i−2i002i−2i2-22-20000000002i−2i0000002-22-20002i−2i0000000000000000000000000000
χ582-2-222-22-22i−2i2i−2i2-22-22i−2i2i−2i2i−2i2i−2i002i−2i2-22-2000000000−2i2i000000-22-22000−2i2i0000000000000000000000000000
χ592-2-222-22-22i−2i2i−2i2-22-2−2i2i2i−2i2i−2i−2i2i00−2i2i-22-2200000002-200002-22i−2i000002i−2i000000000000000000000000000000
χ602-2-222-22-22i−2i2i−2i2-22-2−2i2i2i−2i2i−2i−2i2i00−2i2i-22-220000000-220000-22−2i2i00000−2i2i000000000000000000000000000000
χ612-2-222-22-22i−2i2i−2i-22-222i−2i−2i2i−2i2i2i−2i00−2i2i-222-200000002-20000-22−2i2i000002i−2i000000000000000000000000000000
χ622-2-222-22-22i−2i2i−2i-22-222i−2i−2i2i−2i2i2i−2i00−2i2i-222-20000000-2200002-22i−2i00000−2i2i000000000000000000000000000000
χ632-2-222-22-22i−2i2i−2i-22-22−2i2i−2i2i−2i2i−2i2i002i−2i2-2-220000000002i−2i000000-222-2000−2i2i0000000000000000000000000000
χ642-2-222-22-22i−2i2i−2i-22-22−2i2i−2i2i−2i2i−2i2i002i−2i2-2-22000000000−2i2i0000002-2-220002i−2i0000000000000000000000000000
χ652-2-222-22-2−2i2i−2i2i2-22-22i−2i−2i2i−2i2i2i−2i002i−2i-22-2200000002-200002-2−2i2i00000−2i2i000000000000000000000000000000
χ662-2-222-22-2−2i2i−2i2i2-22-22i−2i−2i2i−2i2i2i−2i002i−2i-22-220000000-220000-222i−2i000002i−2i000000000000000000000000000000
χ672-2-222-22-2−2i2i−2i2i2-22-2−2i2i−2i2i−2i2i−2i2i00−2i2i2-22-20000000002i−2i000000-22-220002i−2i0000000000000000000000000000
χ682-2-222-22-2−2i2i−2i2i2-22-2−2i2i−2i2i−2i2i−2i2i00−2i2i2-22-2000000000−2i2i0000002-22-2000−2i2i0000000000000000000000000000
χ692-2-222-22-2−2i2i−2i2i-22-222i−2i2i−2i2i−2i2i−2i00−2i2i2-2-220000000002i−2i0000002-2-22000−2i2i0000000000000000000000000000
χ702-2-222-22-2−2i2i−2i2i-22-222i−2i2i−2i2i−2i2i−2i00−2i2i2-2-22000000000−2i2i000000-222-20002i−2i0000000000000000000000000000
χ712-2-222-22-2−2i2i−2i2i-22-22−2i2i2i−2i2i−2i−2i2i002i−2i-222-200000002-20000-222i−2i00000−2i2i000000000000000000000000000000
χ722-2-222-22-2−2i2i−2i2i-22-22−2i2i2i−2i2i−2i−2i2i002i−2i-222-20000000-2200002-2−2i2i000002i−2i000000000000000000000000000000
χ7344-44-44-4-400000000440000-4-40000000000000000000000000000000000000022−22000022−220000000000000000
χ7444-44-44-4-400000000440000-4-400000000000000000000000000000000000000−22220000−22220000000000000000
χ7544-44-44-4-400000000-4-4000044000000000000000000000000000000000000002i2−2i20000−2i22i20000000000000000
χ7644-44-44-4-400000000-4-400004400000000000000000000000000000000000000−2i22i200002i2−2i20000000000000000
χ7744-4-44-4-444i−4i−4i4i4i−4i−4i4i00-444-40000000000000000000000000000000000000000000000000000000000000000
χ7844-4-44-4-444i−4i−4i4i−4i4i4i−4i004-4-440000000000000000000000000000000000000000000000000000000000000000
χ7944-4-44-4-44−4i4i4i−4i4i−4i−4i4i004-4-440000000000000000000000000000000000000000000000000000000000000000
χ8044-4-44-4-44−4i4i4i−4i−4i4i4i−4i00-444-40000000000000000000000000000000000000000000000000000000000000000
χ814-444-4-4-44000000004i−4i0000−4i4i00000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i000000000000000000
χ824-444-4-4-44000000004i−4i0000−4i4i0000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i000000000000000000
χ834-444-4-4-4400000000−4i4i00004i−4i00000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i000000000000000000
χ844-444-4-4-4400000000−4i4i00004i−4i0000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i000000000000000000
χ85888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000000000000000000

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