Finite Group Databasebeta

← Group #224582

Character table — Group #224582

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11111111222222222222222222224444444444444444444444444444448888888888888888888888888888888161616161616
order12222222222244444444444444444444444444444444444444888888884444444444444444444888888888888224444
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
χ51111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111111-111-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-1
χ61111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-111
χ71111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111
χ81111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1111111-1-1-1-11111-1-1-1-1111111111-1-11-1-1
χ9111111111111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-1-11111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-1
χ10111111111111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-11-11
χ11111111111111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-11-11
χ12111111111111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111111111-1-1-1-11111-1-11-11-1
χ13111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1111111111111111111-1111-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-11
χ14111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1111-1
χ15111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1111-1
χ16111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11111111111-1-1-1-111111111-1-1-1-1-11-1-1-11
χ1711111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-11-1-11
χ1811111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1111ii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii-11-111-1
χ1911111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1111−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−i-11-111-1
χ2011111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-11-1-11
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111iiii−i−i−i−iiiii−i−i−i−i1-111-1-1-1−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii11-1-11-1
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-111−i−iiiii−i−i−i−iii−i−iiiii−i−iii−i−i-1-111-11
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-111ii−i−i−i−iiiii−i−iii−i−i−i−iii−i−iii-1-111-11
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111−i−i−i−iiiii−i−i−i−iiiii1-111-1-1-1ii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−i11-1-11-1
χ2511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i-1-1111-1-1ii−i−i−i−iii−i−iii−i−iiiii−i−i−i−iii-1111-1-1
χ2611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i1-1-1-111
χ2711111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii1-1-1-111
χ2811111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii-1-1111-1-1−i−iiiii−i−iii−i−iii−i−i−i−iiiii−i−i-1111-1-1
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1111-1-1-1−i−iii−i−iiiii−i−i−i−iii−i−iiiii−i−i-1-1-1111
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-1-111−i−iii−i−iiiii−i−iii−i−iii−i−i−i−iii111-1-1-1
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-1-111ii−i−iii−i−i−i−iii−i−iii−i−iiiii−i−i111-1-1-1
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1111-1-1-1ii−i−iii−i−i−i−iiiii−i−iii−i−i−i−iii-1-1-1111
χ33222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2220000000000000000-2-200-200000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-20000000000000000-2200200000000000000000000000000000000
χ35222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-200000000000000002200-200000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000002-200200000000000000000000000000000000
χ3722222222-2-2-2-2222222222222222222-2-2-2-2-2-22222-2-20000000000000000-2-200-200000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-2-2-2220000000000000000-2200200000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222-2-2-2-2222200000000000000002200-200000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2222222-2-2-2-200000000000000002-200200000000000000000000000000000000
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χ8244-444-4-4-4-4-444000000000000-4-44400-44000000000000000000000000000000000000000000000000000000000000000
χ8344-4-4-444-400000000000000004i−4i−4i4i000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000000000000
χ8444-4-4-444-400000000000000004i−4i−4i4i00000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000000000
χ8544-4-4-444-40000000000000000−4i4i4i−4i000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000000000000
χ8644-4-4-444-40000000000000000−4i4i4i−4i00000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000000000000
χ874-44-44-44-400004-4-444i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000
χ884-44-44-44-400004-4-44−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000
χ894-44-44-44-40000-444-44i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000
χ904-44-44-44-40000-444-4−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000
χ914-4-44-4-4444-44-4000000000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000
χ924-4-44-4-4444-44-400000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000
χ934-4-44-4-444-44-440000000000000000000000000000000000000022−22−2222−222222−220000000000000000000000000000000000000
χ944-4-44-4-444-44-4400000000000000000000000000000000000000−222222−2222−22−22220000000000000000000000000000000000000
χ958-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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