Finite Group Databasebeta

← Group #207446

Character table — Group #207446

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222444444444444444444444444444444442244444444444444222244444444444488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1711111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-111-1-1-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ1811111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ1911111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-111-1-11111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ2011111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-111-1-11111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ2111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii
χ2211111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i
χ2311111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-11111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i
χ2411111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-11111-1-1-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii
χ2511111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii
χ2611111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i
χ2711111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i
χ2811111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-111-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-111-1-111-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-111-1-111-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-111-1-111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i
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χ7422-2-22-2-222i−2i−2i2i2i−2i−2i2i2-2-222i−2i−2i2i-222-22i−2i−2i2i-222-22i−2i−2i2i000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ00000000
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χ7722-2-22-2-222i−2i−2i2i2i−2i−2i2i-222-22i−2i−2i2i-222-2−2i2i2i−2i2-2-22−2i2i2i−2i000000000000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ3
χ7822-2-22-2-222i−2i−2i2i2i−2i−2i2i-222-22i−2i−2i2i-222-2−2i2i2i−2i2-2-22−2i2i2i−2i00000000000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3
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χ8122-2-22-2-22−2i2i2i−2i−2i2i2i−2i2-2-222i−2i−2i2i2-2-222i−2i−2i2i2-2-22−2i2i2i−2i0000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ300000000
χ8222-2-22-2-22−2i2i2i−2i−2i2i2i−2i2-2-222i−2i−2i2i2-2-222i−2i−2i2i2-2-22−2i2i2i−2i000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ300000000
χ8322-2-22-2-22−2i2i2i−2i−2i2i2i−2i2-2-22−2i2i2i−2i-222-2−2i2i2i−2i-222-2−2i2i2i−2i0000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ300000000
χ8422-2-22-2-22−2i2i2i−2i−2i2i2i−2i2-2-22−2i2i2i−2i-222-2−2i2i2i−2i-222-2−2i2i2i−2i000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ300000000
χ8522-2-22-2-22−2i2i2i−2i−2i2i2i−2i-222-22i−2i−2i2i2-2-22−2i2i2i−2i-222-22i−2i−2i2i000000000000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ
χ8622-2-22-2-22−2i2i2i−2i−2i2i2i−2i-222-22i−2i−2i2i2-2-22−2i2i2i−2i-222-22i−2i−2i2i00000000000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ
χ8722-2-22-2-22−2i2i2i−2i−2i2i2i−2i-222-2−2i2i2i−2i-222-22i−2i−2i2i2-2-222i−2i−2i2i000000000000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ
χ8822-2-22-2-22−2i2i2i−2i−2i2i2i−2i-222-2−2i2i2i−2i-222-22i−2i−2i2i2-2-222i−2i−2i2i00000000000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ
χ894-444-4-4-444i−4i4i−4i−4i4i−4i4i000000000000000000000000004i−4i4-40000000000000000000000000000000000000000000000000000000000
χ904-444-4-4-444i−4i4i−4i−4i4i−4i4i00000000000000000000000000−4i4i-440000000000000000000000000000000000000000000000000000000000
χ914-444-4-4-44−4i4i−4i4i4i−4i4i−4i000000000000000000000000004i−4i-440000000000000000000000000000000000000000000000000000000000
χ924-444-4-4-44−4i4i−4i4i4i−4i4i−4i00000000000000000000000000−4i4i4-40000000000000000000000000000000000000000000000000000000000
χ934-44-44-44-44i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000004-44i−4i000000000000000000000000000000000000000000000000
χ944-44-44-44-44i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000-44−4i4i000000000000000000000000000000000000000000000000
χ954-44-44-44-4−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000004-4−4i4i000000000000000000000000000000000000000000000000
χ964-44-44-44-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000-444i−4i000000000000000000000000000000000000000000000000
χ974-4-4444-4-44444-4-4-4-40000000000000000000000000000004-44-4000000000000000000000000000000000000000000000000000000
χ984-4-4444-4-44444-4-4-4-4000000000000000000000000000000-44-44000000000000000000000000000000000000000000000000000000
χ994-4-4444-4-4-4-4-4-444440000000000000000000000000000004-4-44000000000000000000000000000000000000000000000000000000
χ1004-4-4444-4-4-4-4-4-44444000000000000000000000000000000-444-4000000000000000000000000000000000000000000000000000000
χ1014-4-4-4-444444-4-4-4-4440000000000000000000000004-4000000004-40000000000000000000000000000000000000000000000000000
χ1024-4-4-4-444444-4-4-4-444000000000000000000000000-4400000000-440000000000000000000000000000000000000000000000000000
χ1034-4-4-4-4444-4-44444-4-40000000000000000000000004-400000000-440000000000000000000000000000000000000000000000000000
χ1044-4-4-4-4444-4-44444-4-4000000000000000000000000-44000000004-40000000000000000000000000000000000000000000000000000

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