Finite Group Databasebeta

← Group #224608

Character table — Group #224608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11111111222222222222222222224444444444444444444444444444448888888888888888888888888888888161616161616
order12222222444444444444444444444444444444444488888888888888884444444888888888888888888888888444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
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
χ511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11111-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i111-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii111-1-111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-1-1-1111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i111-1-111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-1-1-1111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11111-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii111-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11-1-11-1-1
χ10111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-11111-111-111
χ11111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-111-111
χ12111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-11111-1-11111-1-11111-1-111111-1-11-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111iiii−i−i−i−iiiii−i−i−i−i1-1-111-1-1ii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiii1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-111ii−i−i−i−i−i−iiiii−i−iiiiiii−i−i−i−i-1111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-111−i−iiiiiii−i−i−i−iii−i−i−i−i−i−iiiii-1111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111−i−i−i−iiiii−i−i−i−iiiii1-1-111-1-1−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i1-1-1-111
χ1711111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-11111111111111111-11-11111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-11-1-11-1
χ1811111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-1111-111-11
χ1911111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-111-1-11111-1-111-1-111-1-1-1-111-1-11-111-11
χ2011111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111111-1-11111-1-11111-1-11111-1-111-11-1-11-1
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-11-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii-11-11-11
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11-1-1-111−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−i1-11-11-1
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11-1-1-111ii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii1-11-11-1
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-11-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i-11-11-11
χ2511111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-11-1-11
χ2611111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-111-111-1
χ2711111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-11111-111-1
χ2811111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11111-1-11111-1-11111-1-1-1-11-1-11
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1111-1-1−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i-1-1111-1
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11-1-111−i−i−i−iiiiiii−i−iiiii−i−i−i−i−i−iii11-1-1-11
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11-1-111iiii−i−i−i−i−i−iii−i−i−i−iiiiiii−i−i11-1-1-11
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1111-1-1iiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iii-1-1111-1
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χ3422222222222222222222-2-222-2-222-2-2-2-222-2-222-2-2220000000000000000-2-2-20000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-222-2-2-2-222-2-2220000000000000000-2220000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-22222-2-222-2-20000000000000000-2220000000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-222-2-222-2-2-2-2-2-22222-2-2-2-22200000000000000002-220000000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-222-2-222-2-222-2-2-2-22222-2-200000000000000002-220000000000000000000000000000000000
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χ762-22-2-22-22-22-222i−2i2i−2i−2i2i−2i2i−2i2i00−2i2i00002i−2i00-22002-20000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000001+i−1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000
χ772-22-2-22-22-22-22−2i2i−2i2i2i−2i2i−2i2i−2i002i−2i0000−2i2i00-22002-200000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000−1+i1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000
χ782-22-2-22-22-22-22−2i2i−2i2i2i−2i2i−2i2i−2i002i−2i0000−2i2i00-22002-20000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000001−i−1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000
χ792-22-2-22-22-22-22−2i2i−2i2i2i−2i2i−2i−2i2i00−2i2i00002i−2i002-200-2200000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000−1−i1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i−1−i1+i000000
χ802-22-2-22-22-22-22−2i2i−2i2i2i−2i2i−2i−2i2i00−2i2i00002i−2i002-200-220000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000001+i−1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i1+i−1−i000000
χ814444-4-4-4-44-4-444-4-444-4-44000000000000000000000000000000000000000000000000000000000000000000000000000
χ824444-4-4-4-44-4-44-444-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ834444-4-4-4-4-444-44-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ844444-4-4-4-4-444-4-444-44-4-44000000000000000000000000000000000000000000000000000000000000000000000000000
χ8544-4-4-4-4440000000000004444-4-4-4-4-4400000000000000000000000000000000000000000000000000000000000000000
χ8644-4-4-4-444000000000000-4-4-4-44444-4400000000000000000000000000000000000000000000000000000000000000000
χ874-4-444-4-440000000000004i−4i00−4i4i0000000000000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000
χ884-4-444-4-440000000000004i−4i00−4i4i000000000000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000
χ894-4-444-4-44000000000000−4i4i004i−4i0000000000000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000
χ904-4-444-4-44000000000000−4i4i004i−4i000000000000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000
χ914-4-44-444-4000000000000004i−4i00−4i4i000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000000000000
χ924-4-44-444-4000000000000004i−4i00−4i4i00000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000000000
χ934-4-44-444-400000000000000−4i4i004i−4i000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000000000000
χ944-4-44-444-400000000000000−4i4i004i−4i00000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000000000000
χ9588-8-888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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