Finite Group Databasebeta

← Group #164913

Character table — Group #164913

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11111111222222222222222222224444444444444444444444444444448888888888888888888888888888888161616161616
order12222222222244444444444444444444444444444488888888888888882444444888888888888888888888888224444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11111-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-11-1-111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-11-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11111-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii1-111-1-1
χ9111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111111111111111-1-11111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-11-1-11
χ10111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-11111-1-1111111-111-1
χ11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ12111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-11111-1-11111-1-11111-1-11-1-11
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i-1-1111-1-1ii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiii-111-11-1
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111ii−i−i−i−i−i−iiiii−i−iiiiiii−i−i−i−i1-1-11-11
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111−i−iiiiiii−i−i−i−iii−i−i−i−i−i−iiiii1-1-11-11
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii-1-1111-1-1−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i-111-11-1
χ1711111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111111111111-1111-111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-11-1-1-11-1
χ1811111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-111-1111-11
χ1911111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1-1-1-1-111-1-11111-1-111-1-111-1-1-1-111-1-1-1111-11
χ2011111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11111-1-11111-1-11111-1-11111-1-1111-1-1-11-1
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−iiiii−i−i−i−i-1111-1-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-1-11
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−i−i−i−i−iiiii-11-1-1-111−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−i-1-1111-1
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiiiiiii−i−i−i−i-11-1-1-111ii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii-1-1111-1
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiii−i−i−i−iiiii-1111-1-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i11-1-1-11
χ2511111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111111111111111111-111-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-11-11-1-1
χ2611111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-11-11-111
χ2711111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1111-11-111
χ2811111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1111111-1-11111-1-11111-1-11111-1-1-11-11-1-1
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i1-111-1-1-1−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i-1-1-1111
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-111−i−i−i−iiiiiii−i−iiiii−i−i−i−i−i−iii111-1-1-1
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-111iiii−i−i−i−i−i−iii−i−i−i−iiiiiii−i−i111-1-1-1
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii1-111-1-1-1iiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iii-1-1-1111
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χ874-444-4-44-40000000000004i−4i−4i4i000000000000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000
χ884-444-4-44-40000000000004i−4i−4i4i00000000000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000
χ894-444-4-44-4000000000000−4i4i4i−4i000000000000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000
χ904-444-4-44-4000000000000−4i4i4i−4i00000000000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000
χ914-4-4-4-44444-4-444-4-444-4-44000000000000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-4-44444-4-44-444-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ934-4-4-4-4444-444-44-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ944-4-4-4-4444-444-4-444-44-4-44000000000000000000000000000000000000000000000000000000000000000000000000000
χ958-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.