Finite Group Databasebeta

← Group #392864

Character table — Group #392864

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222244444444444444448888888888888888222244444444444444448888888888888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ11111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ12111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ13111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ1711-11-1-11-111-1-1ii−i−i1-1ii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-111-1-1i−iii−i−ii−i11-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-11-1i−ii−i1-11-1i−ii−i1-1
χ1811-11-1-11-111-1-1ii−i−i1-1ii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-111-1-1i−iii−i−ii−i11-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1-11−ii−ii-11-11−ii−ii-11
χ1911-11-1-11-111-1-1ii−i−i1-1ii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1-1-111i−i−i−iiii−i-1-111−i−iiiii−i−i11-1-1−i−i−i−iiiii-1-1-1-111111-1i−ii−i1-1-11−ii−ii-11
χ2011-11-1-11-111-1-1ii−i−i1-1ii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1-1-111i−i−i−iiii−i-1-111−i−iiiii−i−i11-1-1−i−i−i−iiiii-1-1-1-11111-11−ii−ii-111-1i−ii−i1-1
χ2111-11-1-11-111-1-1ii−i−i1-1ii−i−i11-1-11-1−i−i−i−iiiii-1-1-1-1111111-1-1i−iii−i−ii−i11-1-1ii−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-111111-1−iii−i-111-1i−i−ii-11
χ2211-11-1-11-111-1-1ii−i−i1-1ii−i−i11-1-11-1−i−i−i−iiiii-1-1-1-1111111-1-1i−iii−i−ii−i11-1-1ii−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-11111-11i−i−ii1-1-11−iii−i1-1
χ2311-11-1-11-111-1-1ii−i−i1-1ii−i−i11-1-11-1−i−i−i−iiiii-1-1-1-11111-1-111i−i−i−iiii−i-1-111−i−iii−i−iii-1-111iiii−i−i−i−i1111-1-1-1-11-1−iii−i-11-11−iii−i1-1
χ2411-11-1-11-111-1-1ii−i−i1-1ii−i−i11-1-11-1−i−i−i−iiiii-1-1-1-11111-1-111i−i−i−iiii−i-1-111−i−iii−i−iii-1-111iiii−i−i−i−i1111-1-1-1-1-11i−i−ii1-11-1i−i−ii-11
χ2511-11-1-11-111-1-1−i−iii1-1−i−iii11-1-11-1iiii−i−i−i−i-1-1-1-1111111-1-1−ii−i−iii−ii11-1-1−i−iiiii−i−i-1-111iiii−i−i−i−i-1-1-1-111111-1i−i−ii-111-1−iii−i-11
χ2611-11-1-11-111-1-1−i−iii1-1−i−iii11-1-11-1iiii−i−i−i−i-1-1-1-1111111-1-1−ii−i−iii−ii11-1-1−i−iiiii−i−i-1-111iiii−i−i−i−i-1-1-1-11111-11−iii−i1-1-11i−i−ii1-1
χ2711-11-1-11-111-1-1−i−iii1-1−i−iii11-1-11-1iiii−i−i−i−i-1-1-1-11111-1-111−iiii−i−i−ii-1-111ii−i−iii−i−i-1-111−i−i−i−iiiii1111-1-1-1-11-1i−i−ii-11-11i−i−ii1-1
χ2811-11-1-11-111-1-1−i−iii1-1−i−iii11-1-11-1iiii−i−i−i−i-1-1-1-11111-1-111−iiii−i−i−ii-1-111ii−i−iii−i−i-1-111−i−i−i−iiiii1111-1-1-1-1-11−iii−i1-11-1−iii−i-11
χ2911-11-1-11-111-1-1−i−iii1-1−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-111-1-1−ii−i−iii−ii11-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-11-1−ii−ii1-11-1−ii−ii1-1
χ3011-11-1-11-111-1-1−i−iii1-1−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-111-1-1−ii−i−iii−ii11-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1-11i−ii−i-11-11i−ii−i-11
χ3111-11-1-11-111-1-1−i−iii1-1−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-1-1-111−iiii−i−i−ii-1-111ii−i−i−i−iii11-1-1iiii−i−i−i−i-1-1-1-111111-1−ii−ii1-1-11i−ii−i-11
χ3211-11-1-11-111-1-1−i−iii1-1−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-1-1-111−iiii−i−i−ii-1-111ii−i−i−i−iii11-1-1iiii−i−i−i−i-1-1-1-11111-11i−ii−i-111-1−ii−ii1-1
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χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000220000-2-20000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ35222222222222-2-2-2-2-2-22222-2-2-2-2-2-200000000000000000000-2-200002200000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ36222222222222-2-2-2-2-2-22222-2-2-2-2-2-200000000000000000000-2-20000220000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ3722222222-2-2-2-22222222222-2-2-2-22222222222222222220000-2-20000-2-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000
χ3822222222-2-2-2-22222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000-2-20000-2-2000000002222222200000000000000000000000000000000
χ3922222222-2-2-2-22222-2-2-2-2-2-22222-2-200000000000000002222-2-2222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ4022222222-2-2-2-22222-2-2-2-2-2-22222-2-20000000000000000-2-2-2-2-2-2-2-2-2-222222222220000000000000000000000000000000000000000
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χ4222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000022000022000000002222-2-2-2-200000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-222222222-2-20000000000000000222222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-222222222-2-20000000000000000-2-2-2-2222222-2-22222-2-2-2-20000000000000000000000000000000000000000
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χ822-2-2-2-2222-222-20000220000-222-2-2-2000000002i2i−2i−2i−2i−2i2i2i-222-2000000002-2-2200000000−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ832-2-2-2-2222-222-20000220000-222-2-2-200000000−2i−2i2i2i2i2i−2i−2i2-2-2200000000-222-2000000002i−2i−2i2i00000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ842-2-2-2-2222-222-20000220000-222-2-2-200000000−2i−2i2i2i2i2i−2i−2i-222-2000000002-2-22000000002i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ852-2-2-2-2222-222-20000-2-200002-2-222222-2-2-2-222000000000000002-2-22000000-222-2-222-2000000000000-222-22-2-220000000000000000
χ862-2-2-2-2222-222-20000-2-200002-2-222222-2-2-2-22200000000000000-222-20000002-2-22-222-20000000000002-2-22-222-20000000000000000
χ872-2-2-2-2222-222-20000-2-200002-2-2222-2-22222-2-2000000000000002-2-22000000-222-22-2-220000000000002-2-22-222-20000000000000000
χ882-2-2-2-2222-222-20000-2-200002-2-2222-2-22222-2-200000000000000-222-20000002-2-222-2-22000000000000-222-22-2-220000000000000000
χ89444-4-44-4-400004-44-400000000000022−2222−2222−2222−2222−2222−2222−2222−22000000000000000000000000000000000000000000000000000000000000
χ90444-4-44-4-400004-44-4000000000000−2222−2222−2222−2222−2222−2222−2222−2222000000000000000000000000000000000000000000000000000000000000
χ91444-4-44-4-40000-44-4400000000000022−2222−2222−2222−22−2222−2222−2222−2222000000000000000000000000000000000000000000000000000000000000
χ92444-4-44-4-40000-44-44000000000000−2222−2222−2222−222222−2222−2222−2222−22000000000000000000000000000000000000000000000000000000000000
χ9344-4-44-4-4400004i−4i−4i4i0000000000002i2−2i22i2−2i2−2i22i2−2i22i222−2222−22−2222−2222000000000000000000000000000000000000000000000000000000000000
χ9444-4-44-4-4400004i−4i−4i4i000000000000−2i22i2−2i22i22i2−2i22i2−2i2−2222−222222−2222−22000000000000000000000000000000000000000000000000000000000000
χ9544-4-44-4-440000−4i4i4i−4i0000000000002i2−2i22i2−2i2−2i22i2−2i22i2−2222−222222−2222−22000000000000000000000000000000000000000000000000000000000000
χ9644-4-44-4-440000−4i4i4i−4i000000000000−2i22i2−2i22i22i2−2i22i2−2i222−2222−22−2222−2222000000000000000000000000000000000000000000000000000000000000
χ974-444-4-4-4400000000004-44-40000002i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ984-444-4-4-4400000000004-44-4000000−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ994-444-4-4-440000000000-44-440000002i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ1004-444-4-4-440000000000-44-44000000−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ1014-4-4444-4-400000000004i−4i−4i4i00000022−22−2222−222222−22−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ1024-4-4444-4-400000000004i−4i−4i4i000000−222222−2222−22−22222i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ1034-4-4444-4-40000000000−4i4i4i−4i00000022−22−2222−222222−222i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ1044-4-4444-4-40000000000−4i4i4i−4i000000−222222−2222−22−2222−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000

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