Finite Group Databasebeta

← Group #190683

Character table — Group #190683

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222444444444444444444444444444444442244444444444444444444444444444488888888888888888888888888888888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i
χ91111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ121111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ1711111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ1811111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ1911111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ2011111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ2111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ2211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-11111-1-111-1-1-1-111-1-111-1-111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1
χ2311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111-1-111-1-11111-1-111-1-111-1-111-1-1-1-111-1-111-1-111-1-11111-1-111-1-1
χ2411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111-1-111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-111-1-111-1-1-1-111-1-111
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-1
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1
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χ3822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-222-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
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χ4022222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000000
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χ802-22-2-22-222i−2i2i−2i2i−2i2i−2i−2i2i−2i2i-22-22−2i2i−2i2i0000-22-2200002-22i−2i00000000000000000000000000000000000000000000−22i2−i2−i2i22−2−i2i22−2−22i2−i2
χ812-22-2-22-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i-22-222i−2i2i−2i0000-22-2200002-2−2i2i000000000000000000000000000000000000000000002−2i2−i2−i2i2−22−i2i2−222−2i2−i2
χ822-22-2-22-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i-22-222i−2i2i−2i0000-22-2200002-2−2i2i00000000000000000000000000000000000000000000−22−i2i2i2−i22−2i2−i22−2−22−i2i2
χ832-22-2-22-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i-22-22−2i2i−2i2i00002-22-20000-222i−2i00000000000000000000000000000000000000000000i2−i2−222−2−i2i2−22i2−i2−i2i22−2
χ842-22-2-22-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i-22-22−2i2i−2i2i00002-22-20000-222i−2i00000000000000000000000000000000000000000000−i2i22−2−22i2−i22−2−i2i2i2−i2−22
χ852-22-2-22-22−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-22i−2i2i−2i0000-22-220000-222i−2i000000000000000000000000000000000000000000002−2i2−i2i2−i22−2−i2i2−22−22−i2i2
χ862-22-2-22-22−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-22i−2i2i−2i0000-22-220000-222i−2i00000000000000000000000000000000000000000000−22−i2i2−i2i2−22i2−i22−22−2i2−i2
χ872-22-2-22-22−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-2−2i2i−2i2i00002-22-200002-2−2i2i00000000000000000000000000000000000000000000i2−i2−22−22i2−i2−22i2−i2i2−i2−22
χ882-22-2-22-22−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-2−2i2i−2i2i00002-22-200002-2−2i2i00000000000000000000000000000000000000000000−i2i22−22−2−i2i22−2−i2i2−i2i22−2
χ894444-4-4-4-44-4-444-4-44000000004-4-4400004-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ904444-4-4-4-44-4-444-4-4400000000-444-40000-444-400000000000000000000000000000000000000000000000000000000000000000000
χ914444-4-4-4-4-444-4-444-4000000004-4-440000-444-400000000000000000000000000000000000000000000000000000000000000000000
χ924444-4-4-4-4-444-4-444-400000000-444-400004-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ9344-4-4-4-4444-4-44-444-4000000000000000000000000000000004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ9444-4-4-4-4444-4-44-444-400000000000000000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ9544-4-4-4-444-444-44-4-44000000000000000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ9644-4-4-4-444-444-44-4-4400000000000000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ974-4-444-4-444i4i−4i−4i−4i−4i4i4i0000000000004i−4i−4i4i00004-4-440000000000000000000000000000000000000000000000000000000000000000
χ984-4-444-4-444i4i−4i−4i−4i−4i4i4i000000000000−4i4i4i−4i0000-444-40000000000000000000000000000000000000000000000000000000000000000
χ994-4-444-4-44−4i−4i4i4i4i4i−4i−4i0000000000004i−4i−4i4i0000-444-40000000000000000000000000000000000000000000000000000000000000000
χ1004-4-444-4-44−4i−4i4i4i4i4i−4i−4i000000000000−4i4i4i−4i00004-4-440000000000000000000000000000000000000000000000000000000000000000
χ1014-4-44-444-44i−4i4i−4i−4i4i−4i4i4-4-44−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-44-444-44i−4i4i−4i−4i4i−4i4i-444-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-44-444-4−4i4i−4i4i4i−4i4i−4i4-4-444i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-444-4−4i4i−4i4i4i−4i4i−4i-444-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000000000

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