Finite Group Databasebeta

← Group #196670

Character table — Group #196670

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222244444444444444444444444444444444222244444444888888888888888888888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1-111-1-11-1iiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-11-1-111-11−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii1-111-1-11-1−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-11-1-111-11iiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1-1-1-1111-1ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1111-1-1-11−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1-1-1-1111-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1111-1-1-11ii−i−i−i−iii
χ1711111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-1-11i−ii−ii−ii−i
χ1811111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-111-1−ii−ii−ii−ii
χ1911111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-1-11−ii−ii−ii−ii
χ2011111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-11-111-1i−ii−ii−ii−i
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-11-1-11-11-1-11-11
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111-111-11-111-11-1
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1111-1-11-1-1-11-111-11-1
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1111-11-1-11-11
χ2511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11-11-11i−i−iii−i−ii
χ2611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-111-11-11-1−iii−i−iii−i
χ2711111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11-11-11−iii−i−iii−i
χ2811111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-11-11-1i−i−iii−i−ii
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-111-1-1-11-1-11-111-1
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11-1-1111-111-11-1-11
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-1-1-1-111-11-1-11
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1-11111-1-11-111-1
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χ35222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2222222-2-2000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-22222-2-222222222-2-2-2-22222-2-2-2-222-2-222-2-2-2-2000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222222222-2-22222-2-2-2-222222222-2-222-2-222-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-2-2-22222222222-2-2-2-2-2-2-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
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χ672-222-22-2-20000-2-22200002i−2i2i−2i00−2i2i−2i2i−2i−2i2i2i0000-22-2200002-2002i−2i00002−22−2i2−i2i2−i2−22−22−i2i2−i2i2−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000000000
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χ702-222-22-2-20000-2-2220000−2i2i−2i2i002i−2i2i−2i2i2i−2i−2i0000-22-2200002-200−2i2i0000−22−22i2−i2i2−i22−22−2−i2i2−i2i2−i2i2−i2i22−22−2i2−i2i2−i2−22−220000000000000000
χ712-222-22-2-20000-2-2220000−2i2i−2i2i00−2i2i−2i2i2i2i−2i−2i00002-22-20000-22002i−2i0000i2−i2i2−i2−22−22−i2i2−i2i22−22−2−22−22i2−i2i2−i22−22−2−i2i2−i2i20000000000000000
χ722-222-22-2-20000-2-2220000−2i2i−2i2i00−2i2i−2i2i2i2i−2i−2i00002-22-20000-22002i−2i0000−i2i2−i2i22−22−2i2−i2i2−i2−22−222−22−2−i2i2−i2i2−22−22i2−i2i2−i20000000000000000
χ732-2-22-2-22222-2-2000000002-2-22222-2-22000000002-2-22-2-2000000002-22-2000000002i−2i−2i2i−2i2i2i−2i00000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ742-2-22-2-22222-2-2000000002-2-22222-2-22000000002-2-22-2-2000000002-22-200000000−2i2i2i−2i2i−2i−2i2i000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ752-2-22-2-22222-2-2000000002-2-2222-222-200000000-222-2-2-200000000-22-222i−2i−2i2i−2i2i2i−2i000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ762-2-22-2-22222-2-2000000002-2-2222-222-200000000-222-2-2-200000000-22-22−2i2i2i−2i2i−2i−2i2i00000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ772-2-22-2-22222-2-200000000-222-2-2-22-2-2200000000-222-22200000000-222-2000000002-2-22-222-2000000002-2-22-222-20000000000000000
χ782-2-22-2-22222-2-200000000-222-2-2-22-2-2200000000-222-22200000000-222-200000000-222-22-2-2200000000-222-22-2-220000000000000000
χ792-2-22-2-22222-2-200000000-222-2-2-2-222-2000000002-2-2222000000002-2-222-2-22-222-200000000-222-22-2-22000000000000000000000000
χ802-2-22-2-22222-2-200000000-222-2-2-2-222-2000000002-2-2222000000002-2-22-222-22-2-22000000002-2-22-222-2000000000000000000000000
χ812-2-22-2-222-2-222000000002-2-22-2-22-2-22000000002-2-222200000000-22-222-2-222-2-22000000002-2-222-2-22000000000000000000000000
χ822-2-22-2-222-2-222000000002-2-22-2-22-2-22000000002-2-222200000000-22-22-222-2-222-200000000-222-2-222-2000000000000000000000000
χ832-2-22-2-222-2-222000000002-2-22-2-2-222-200000000-222-222000000002-22-2000000002-2-222-2-2200000000-222-2-222-20000000000000000
χ842-2-22-2-222-2-222000000002-2-22-2-2-222-200000000-222-222000000002-22-200000000-222-2-222-2000000002-2-222-2-220000000000000000
χ852-2-22-2-222-2-22200000000-222-2222-2-2200000000-222-2-2-2000000002-2-222i−2i−2i2i2i−2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ862-2-22-2-222-2-22200000000-222-2222-2-2200000000-222-2-2-2000000002-2-22−2i2i2i−2i−2i2i2i−2i000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ872-2-22-2-222-2-22200000000-222-222-222-2000000002-2-22-2-200000000-222-2000000002i−2i−2i2i2i−2i−2i2i000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ882-2-22-2-222-2-22200000000-222-222-222-2000000002-2-22-2-200000000-222-200000000−2i2i2i−2i−2i2i2i−2i00000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ89444-4-4-4-444-44-44i−4i4i−4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ90444-4-4-4-444-44-4−4i4i−4i4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ91444-4-4-4-44-44-444i−4i4i−4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ92444-4-4-4-44-44-44−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9344-4-4-444-4000000004i−4i−4i4i00004-400004i−4i4i−4i000000004-4000000000000000000000000000000000000000000000000000000000000
χ9444-4-4-444-4000000004i−4i−4i4i0000-440000−4i4i−4i4i00000000-44000000000000000000000000000000000000000000000000000000000000
χ9544-4-4-444-400000000−4i4i4i−4i00004-40000−4i4i−4i4i000000004-4000000000000000000000000000000000000000000000000000000000000
χ9644-4-4-444-400000000−4i4i4i−4i0000-4400004i−4i4i−4i00000000-44000000000000000000000000000000000000000000000000000000000000
χ974-44-44-44-400004i−4i−4i4i000000004-4000000004i−4i4i−4i0000-44000000000000000000000000000000000000000000000000000000000000
χ984-44-44-44-400004i−4i−4i4i00000000-4400000000−4i4i−4i4i00004-4000000000000000000000000000000000000000000000000000000000000
χ994-44-44-44-40000−4i4i4i−4i000000004-400000000−4i4i−4i4i0000-44000000000000000000000000000000000000000000000000000000000000
χ1004-44-44-44-40000−4i4i4i−4i00000000-44000000004i−4i4i−4i00004-4000000000000000000000000000000000000000000000000000000000000
χ1014-4-4-444-444-4-440000000000000000004-4-444-4-44000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-4-444-444-4-44000000000000000000-444-4-444-4000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-444-44-444-40000000000000000004-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-444-44-444-4000000000000000000-444-44-4-44000000000000000000000000000000000000000000000000000000000000000000

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