Finite Group Databasebeta

← Group #207352

Character table — Group #207352

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222444444444444444444444444444444442244444444444444888888888888888888888888888888888888888888888888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1211111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1711111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-111-1-111-1-1
χ1811111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-1-111-1-111-1-111-1-111
χ1911111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-1-111-1-111-1-111-1-111
χ2011111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-111-1-111-1-111-1-1
χ2111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-11111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii11-1-111-1-1-1-111-1-111
χ2211111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-11111ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-1-111-1-11111-1-111-1-1
χ2311111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-11111−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-1-111-1-11111-1-111-1-1
χ2411111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-11111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1-1-111-1-111
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-11111-1-1-1-111
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1-1-11111-1-1
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1-1-11111-1-1
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-11111-1-1-1-111
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-11111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111-1-11111-1-1
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-11111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-111-1-1-1-111
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-11111-1-1-1-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-111-1-1-1-111
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-11111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111-1-11111-1-1
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χ3722222222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-22222-2-2000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222-2-2000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-222-2-2-2-2-2-222000000000000000000000000000000000000000000000000
χ412222-2-2-2-22222-2-2-2-2000022-2-222-2-222-2-222-2-200002-200000000002-200000000000000000000000000000000002−22−22−22−22−22−22−22−2
χ422222-2-2-2-22222-2-2-2-2000022-2-222-2-222-2-222-2-200002-200000000002-20000000000000000000000000000000000−22−22−22−22−22−22−22−22
χ432222-2-2-2-22222-2-2-2-2000022-2-222-2-2-2-222-2-2220000-220000000000-2200000000000000000000000000000000002−22−22−22−2−22−22−22−22
χ442222-2-2-2-22222-2-2-2-2000022-2-222-2-2-2-222-2-2220000-220000000000-220000000000000000000000000000000000−22−22−22−222−22−22−22−2
χ452222-2-2-2-22222-2-2-2-20000-2-222-2-22222-2-222-2-20000-220000000000-2200000000000000000000000000000000002−22−2−22−222−22−2−22−22
χ462222-2-2-2-22222-2-2-2-20000-2-222-2-22222-2-222-2-20000-220000000000-220000000000000000000000000000000000−22−222−22−2−22−222−22−2
χ472222-2-2-2-22222-2-2-2-20000-2-222-2-222-2-222-2-22200002-200000000002-200000000000000000000000000000000002−22−2−22−22−22−222−22−2
χ482222-2-2-2-22222-2-2-2-20000-2-222-2-222-2-222-2-22200002-200000000002-20000000000000000000000000000000000−22−222−22−22−22−2−22−22
χ492222-2-2-2-2-2-2-2-22222000022-2-2-2-22222-2-2-2-22200002-20000000000-2200000000000000000000000000000000002−2−222−2−222−2−222−2−22
χ502222-2-2-2-2-2-2-2-22222000022-2-2-2-22222-2-2-2-22200002-20000000000-220000000000000000000000000000000000−222−2−222−2−222−2−222−2
χ512222-2-2-2-2-2-2-2-22222000022-2-2-2-222-2-22222-2-20000-2200000000002-200000000000000000000000000000000002−2−222−2−22−222−2−222−2
χ522222-2-2-2-2-2-2-2-22222000022-2-2-2-222-2-22222-2-20000-2200000000002-20000000000000000000000000000000000−222−2−222−22−2−222−2−22
χ532222-2-2-2-2-2-2-2-222220000-2-22222-2-222-2-2-2-2220000-2200000000002-200000000000000000000000000000000002−2−22−222−22−2−22−222−2
χ542222-2-2-2-2-2-2-2-222220000-2-22222-2-222-2-2-2-2220000-2200000000002-20000000000000000000000000000000000−222−22−2−22−222−22−2−22
χ552222-2-2-2-2-2-2-2-222220000-2-22222-2-2-2-22222-2-200002-20000000000-2200000000000000000000000000000000002−2−22−222−2−222−22−2−22
χ562222-2-2-2-2-2-2-2-222220000-2-22222-2-2-2-22222-2-200002-20000000000-220000000000000000000000000000000000−222−22−2−222−2−22−222−2
χ5722-2-222-2-222-2-222-2-222-2-2000000002i−2i2i−2i2i−2i2i−2i22-2-20000002i−2i2i−2i000000000000000000000000002i−2i2i−2i00002-22-20000000000000000
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χ6422-2-222-2-222-2-222-2-2-2-22200000000−2i2i−2i2i−2i2i−2i2i-2-2220000002i−2i2i−2i0000000000000000000000-22-2200002i−2i2i−2i00000000000000000000
χ6522-2-222-2-2-2-222-2-22222-2-2000000002i−2i2i−2i−2i2i−2i2i-2-222000000−2i2i2i−2i00000000000000000000002i−2i−2i2i0000-222-200000000000000000000
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χ6722-2-222-2-2-2-222-2-22222-2-200000000−2i2i−2i2i2i−2i2i−2i-2-2220000002i−2i−2i2i00000000000000000000002i−2i−2i2i00002-2-2200000000000000000000
χ6822-2-222-2-2-2-222-2-22222-2-200000000−2i2i−2i2i2i−2i2i−2i-2-2220000002i−2i−2i2i0000000000000000000000−2i2i2i−2i0000-222-200000000000000000000
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χ742-22-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-22i−2i2i−2i000000002-22-2002-22i−2i000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000000000000000000000000000
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χ772-22-22-22-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i2-22-22i−2i2i−2i00000000-22-2200-22−2i2i00000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000000000000000000
χ782-22-22-22-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i2-22-22i−2i2i−2i00000000-22-2200-22−2i2i0000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000000000000000000
χ792-22-22-22-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i-22-22−2i2i−2i2i00000000-22-22002-22i−2i00000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000000000000000000
χ802-22-22-22-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i-22-22−2i2i−2i2i00000000-22-22002-22i−2i0000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000000000000000000
χ812-22-22-22-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2-22-2−2i2i−2i2i00000000-22-2200-222i−2i00000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000000000000000000
χ822-22-22-22-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2-22-2−2i2i−2i2i00000000-22-2200-222i−2i0000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000000000000000000
χ832-22-22-22-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i-22-222i−2i2i−2i00000000-22-22002-2−2i2i00000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000000000000000000
χ842-22-22-22-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i-22-222i−2i2i−2i00000000-22-22002-2−2i2i0000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000000000000000000
χ852-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-2−2i2i−2i2i000000002-22-2002-2−2i2i0000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000000000000000000000000000
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χ8944-4-4-4-44444-4-4-4-4440000000000004i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ9044-4-4-4-44444-4-4-4-444000000000000−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-4-4-444-4-44444-4-40000000000004i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ9244-4-4-4-444-4-44444-4-4000000000000−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ934-44-4-44-444i−4i4i−4i−4i4i−4i4i00004-4-444i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ944-44-4-44-444i−4i4i−4i−4i4i−4i4i0000-444-4−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ954-44-4-44-44−4i4i−4i4i4i−4i4i−4i00004-4-44−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ964-44-4-44-44−4i4i−4i4i4i−4i4i−4i0000-444-44i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ974-4-444-4-444i−4i−4i4i4i−4i−4i4i4i−4i−4i4i00000000000000004-4-440000000000000000000000000000000000000000000000000000000000000000
χ984-4-444-4-444i−4i−4i4i4i−4i−4i4i−4i4i4i−4i0000000000000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ994-4-444-4-44−4i4i4i−4i−4i4i4i−4i4i−4i−4i4i0000000000000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ1004-4-444-4-44−4i4i4i−4i−4i4i4i−4i−4i4i4i−4i00000000000000004-4-440000000000000000000000000000000000000000000000000000000000000000
χ1014-4-44-444-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000004i−4i004-4000000000000000000000000000000000000000000000000
χ1024-4-44-444-44i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000−4i4i00-44000000000000000000000000000000000000000000000000
χ1034-4-44-444-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000004i−4i00-44000000000000000000000000000000000000000000000000
χ1044-4-44-444-4−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000−4i4i004-4000000000000000000000000000000000000000000000000

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