Finite Group Databasebeta

← Group #393292

Character table — Group #393292

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222244444444444444448888888888888888444444444444444444448888888888888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ17111-1-11-1-111-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−ii−i11-1-1ii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i1-1i−i1-1i−i1-1i−i
χ18111-1-11-1-111-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−ii−i11-1-1ii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii-11−ii-11−ii-11−ii
χ19111-1-11-1-111-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−ii−i-1-111−i−iiii−i-1-111−i−iii11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii1-1i−i1-1i−i-11−ii-11−ii
χ20111-1-11-1-111-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−ii−i-1-111−i−iiii−i-1-111−i−iii11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii-11−ii-11−ii1-1i−i1-1i−i
χ21111-1-11-1-111-1-1ii−i−iii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiii−i11-1-1ii−i−ii−i11-1-1ii−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-1i−i-11−ii1-1i−i-11−ii
χ22111-1-11-1-111-1-1ii−i−iii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiii−i11-1-1ii−i−ii−i11-1-1ii−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-11−ii1-1i−i-11−ii1-1i−i
χ23111-1-11-1-111-1-1ii−i−iii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiii−i-1-111−i−iiii−i-1-111−i−iii-1-111−i−iii1111-1-1-1-1iiii−i−i−i−i1-1i−i-11−ii-11−ii1-1i−i
χ24111-1-11-1-111-1-1ii−i−iii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiii−i-1-111−i−iiii−i-1-111−i−iii-1-111−i−iii1111-1-1-1-1iiii−i−i−i−i-11−ii1-1i−i1-1i−i-11−ii
χ25111-1-11-1-111-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−ii11-1-1−i−iii−ii11-1-1−i−iii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-1−ii1-1−ii1-1−ii1-1−ii
χ26111-1-11-1-111-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−ii11-1-1−i−iii−ii11-1-1−i−iii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-11i−i-11i−i-11i−i-11i−i
χ27111-1-11-1-111-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−ii-1-111ii−i−i−ii-1-111ii−i−i11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i1-1−ii1-1−ii-11i−i-11i−i
χ28111-1-11-1-111-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−ii-1-111ii−i−i−ii-1-111ii−i−i11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i-11i−i-11i−i1-1−ii1-1−ii
χ29111-1-11-1-111-1-1−i−iii−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−ii11-1-1−i−iii−ii11-1-1−i−iii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-1−ii-11i−i1-1−ii-11i−i
χ30111-1-11-1-111-1-1−i−iii−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−ii11-1-1−i−iii−ii11-1-1−i−iii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-11i−i1-1−ii-11i−i1-1−ii
χ31111-1-11-1-111-1-1−i−iii−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−ii-1-111ii−i−i−ii-1-111ii−i−i-1-111ii−i−i1111-1-1-1-1−i−i−i−iiiii1-1−ii-11i−i-11i−i1-1−ii
χ32111-1-11-1-111-1-1−i−iii−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−ii-1-111ii−i−i−ii-1-111ii−i−i-1-111ii−i−i1111-1-1-1-1−i−i−i−iiiii-11i−i1-1−ii1-1−ii-11i−i
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χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002200000000-2-20000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ35222222222222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000-2-2000000002200000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ36222222222222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000-2-200000000220000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ3722222222-2-2-2-22222222222-2-222-2-22222222222222222-2-200000000-2-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000
χ3822222222-2-2-2-22222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2000000002222222200000000000000000000000000000000
χ3922222222-2-2-2-22222-2-2-2-2-2-222-2-2220000000000000000-2-22222-2-2-2-222-2-2-2-222220000000000000000000000000000000000000000
χ4022222222-2-2-2-22222-2-2-2-2-2-222-2-2220000000000000000-2-2-2-2-2-22222222222-2-2-2-20000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-22222-2-222-2-22200000000000000002222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
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χ4322222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222222222-2-2-2-2-2-2-2-222000000002200000000-2-2-2-2222200000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2-222222222220000000022000000002222-2-2-2-200000000000000000000000000000000
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χ8122-2-22-2-22-222-2000000002-2-22-222-2000000002i2i−2i−2i−2i−2i2i2i002i−2i−2i2i000000−2i2i2i−2i00000000−2i2i2i−2i00000000-22-222-22-20000000000000000
χ8222-2-22-2-22-222-2000000002-2-22-222-2000000002i2i−2i−2i−2i−2i2i2i00−2i2i2i−2i0000002i−2i−2i2i00000000−2i2i2i−2i000000002-22-2-22-220000000000000000
χ8322-2-22-2-22-222-2000000002-2-22-222-200000000−2i−2i2i2i2i2i−2i−2i002i−2i−2i2i000000−2i2i2i−2i000000002i−2i−2i2i000000002-22-2-22-220000000000000000
χ8422-2-22-2-22-222-2000000002-2-22-222-200000000−2i−2i2i2i2i2i−2i−2i00−2i2i2i−2i0000002i−2i−2i2i000000002i−2i−2i2i00000000-22-222-22-20000000000000000
χ8522-2-22-2-22-222-200000000-222-22-2-222i2i−2i−2i−2i−2i2i2i000000000000002-2-22000000-222-2−2i2i2i−2i0000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ8622-2-22-2-22-222-200000000-222-22-2-222i2i−2i−2i−2i−2i2i2i00000000000000-222-20000002-2-22−2i2i2i−2i000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ8722-2-22-2-22-222-200000000-222-22-2-22−2i−2i2i2i2i2i−2i−2i000000000000002-2-22000000-222-22i−2i−2i2i000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ8822-2-22-2-22-222-200000000-222-22-2-22−2i−2i2i2i2i2i−2i−2i00000000000000-222-20000002-2-222i−2i−2i2i0000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ894-444-4-4-4400004-44-40000000000002i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ904-444-4-4-4400004-44-4000000000000−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ914-444-4-4-440000-44-440000000000002i2−2i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ924-444-4-4-440000-44-44000000000000−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ934-44-44-44-400004i−4i−4i4i0000000000002i2−2i22i2−2i2−2i22i2−2i22i2−2222−222222−2222−22000000000000000000000000000000000000000000000000000000000000
χ944-44-44-44-400004i−4i−4i4i000000000000−2i22i2−2i22i22i2−2i22i2−2i222−2222−22−2222−2222000000000000000000000000000000000000000000000000000000000000
χ954-44-44-44-40000−4i4i4i−4i0000000000002i2−2i22i2−2i2−2i22i2−2i22i222−2222−22−2222−2222000000000000000000000000000000000000000000000000000000000000
χ964-44-44-44-40000−4i4i4i−4i000000000000−2i22i2−2i22i22i2−2i22i2−2i2−2222−222222−2222−22000000000000000000000000000000000000000000000000000000000000
χ974-4-4444-4-4000000004i−4i4i−4i0000000022−22−222222−22−22222i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ984-4-4444-4-4000000004i−4i4i−4i00000000−222222−22−222222−22−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ994-4-4444-4-400000000−4i4i−4i4i0000000022−22−222222−22−2222−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ1004-4-4444-4-400000000−4i4i−4i4i00000000−222222−22−222222−222i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ1014-4-4-4-4444000000004-4-440000000022−22−2222−222222−2222−22−2222−222222−22000000000000000000000000000000000000000000000000000000000000
χ1024-4-4-4-4444000000004-4-4400000000−222222−2222−22−2222−222222−2222−22−2222000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-4-444400000000-444-40000000022−22−2222−222222−22−222222−2222−22−2222000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-444400000000-444-400000000−222222−2222−22−222222−22−2222−222222−22000000000000000000000000000000000000000000000000000000000000

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