Finite Group Databasebeta

← Group #191940

Character table — Group #191940

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222444444442222444444444444444444444444888888888888888888888888444444444444888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ151111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ1711111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1i−ii−iii−i−iii−i−iii−i−iii−i−ii−ii−i
χ1811111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1i−ii−iii−i−iii−i−i−i−iii−i−iii−ii−ii
χ1911111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii−ii−ii
χ2011111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1−ii−ii−i−iii−i−iiiii−i−iii−i−ii−ii−i
χ2111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111i−ii−i−i−iii−i−iiiii−i−iii−i−i−ii−ii
χ2211111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111ii−i−iii−i−i-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111i−ii−i−i−iii−i−iii−i−iii−i−iiii−ii−i
χ2311111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111−i−iii−i−iii1111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111−ii−iiii−i−iii−i−i−i−iii−i−iiii−ii−i
χ2411111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111−i−iii−i−iii-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111−ii−iiii−i−iii−i−iii−i−iii−i−i−ii−ii
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1ii−i−i−i−iii1111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111i−i−iiii−i−i−i−iiiii−i−i−i−iiii−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1ii−i−i−i−iii-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111i−i−iiii−i−i−i−iii−i−iiiii−i−i−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1−i−iiiii−i−i1111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111−iii−i−i−iiiii−i−i−i−iiiii−i−i−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1−i−iiiii−i−i-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111−iii−i−i−iiiii−i−iii−i−i−i−iiii−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111ii−i−i−i−iii1111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1i−i−ii−i−iiiii−i−iii−i−i−i−iii−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111ii−i−i−i−iii-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1i−i−ii−i−iiiii−i−i−i−iiiii−i−ii−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1−iii−iii−i−i−i−iii−i−iiiii−i−ii−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111−i−iiiii−i−i-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1−iii−iii−i−i−i−iiiii−i−i−i−iii−iii−i
χ33222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222220000000000000000000000000000-2-2-2-200000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000222200000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000002222-2-2-2-20000000000000000000000000000-2-22200000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-22222000000000000000000000000000022-2-200000000000000000000
χ3722222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-222-2-222000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2i2i−2i2i00000000000000000000
χ3822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-222-2-22200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002i−2i2i−2i00000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-22222-2-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000−2i2i2i−2i00000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-22222-2-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000002i−2i−2i2i00000000000000000000
χ412222-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000002-22-22-22-222−2−222−2−222−2−222−2−20000000000000000000000002−22−22−22−20000
χ422222-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000002-22-22-22-2−2−222−2−222−2−222−2−222000000000000000000000000−22−22−22−220000
χ432222-2-2-2-222-2-222-2-222-2-222-2-200000000000000000000-22-22-22-2222−2−222−2−222−2−222−2−2000000000000000000000000−22−22−22−220000
χ442222-2-2-2-222-2-222-2-222-2-222-2-200000000000000000000-22-22-22-22−2−222−2−222−2−222−2−2220000000000000000000000002−22−22−22−20000
χ452222-2-2-2-222-2-222-2-2-2-222-2-222000000000000000000002-22-2-22-2222−2−222−2−2−2−222−2−2220000000000000000000000002−22−2−22−220000
χ462222-2-2-2-222-2-222-2-2-2-222-2-222000000000000000000002-22-2-22-22−2−222−2−22222−2−222−2−2000000000000000000000000−22−222−22−20000
χ472222-2-2-2-222-2-222-2-2-2-222-2-22200000000000000000000-22-222-22-222−2−222−2−2−2−222−2−222000000000000000000000000−22−222−22−20000
χ482222-2-2-2-222-2-222-2-2-2-222-2-22200000000000000000000-22-222-22-2−2−222−2−22222−2−222−2−20000000000000000000000002−22−2−22−220000
χ492222-2-2-2-2-2-222-2-22222-2-2-2-222000000000000000000002i−2i−2i2i2i−2i−2i2i22−2−2−2−22222−2−2−2−222000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ502222-2-2-2-2-2-222-2-22222-2-2-2-222000000000000000000002i−2i−2i2i2i−2i−2i2i−2−22222−2−2−2−22222−2−2000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ512222-2-2-2-2-2-222-2-22222-2-2-2-22200000000000000000000−2i2i2i−2i−2i2i2i−2i22−2−2−2−22222−2−2−2−222000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ522222-2-2-2-2-2-222-2-22222-2-2-2-22200000000000000000000−2i2i2i−2i−2i2i2i−2i−2−22222−2−2−2−22222−2−2000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ532222-2-2-2-2-2-222-2-222-2-22222-2-2000000000000000000002i−2i−2i2i−2i2i2i−2i22−2−2−2−222−2−22222−2−2000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ542222-2-2-2-2-2-222-2-222-2-22222-2-2000000000000000000002i−2i−2i2i−2i2i2i−2i−2−22222−2−222−2−2−2−222000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ552222-2-2-2-2-2-222-2-222-2-22222-2-200000000000000000000−2i2i2i−2i2i−2i−2i2i22−2−2−2−222−2−22222−2−2000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ562222-2-2-2-2-2-222-2-222-2-22222-2-200000000000000000000−2i2i2i−2i2i−2i−2i2i−2−22222−2−222−2−2−2−222000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ5722-2-22-22-22i−2i2i−2i2i−2i2i−2i000000002-22i−2i2-22i−2i000022-2-22i2i−2i−2i00000000000000002-22-22i−2i2i−2i00002-22i−2i0000000000000000000000000000
χ5822-2-22-22-22i−2i2i−2i2i−2i2i−2i000000002-22i−2i2-22i−2i000022-2-22i2i−2i−2i0000000000000000-22-22−2i2i−2i2i0000-22−2i2i0000000000000000000000000000
χ5922-2-22-22-22i−2i2i−2i2i−2i2i−2i000000002-22i−2i2-22i−2i0000-2-222−2i−2i2i2i00000000000000002-22-22i−2i2i−2i0000-22−2i2i0000000000000000000000000000
χ6022-2-22-22-22i−2i2i−2i2i−2i2i−2i000000002-22i−2i2-22i−2i0000-2-222−2i−2i2i2i0000000000000000-22-22−2i2i−2i2i00002-22i−2i0000000000000000000000000000
χ6122-2-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-2−2i2i2-2−2i2i000022-2-2−2i−2i2i2i00000000000000002-22-2−2i2i−2i2i00002-2−2i2i0000000000000000000000000000
χ6222-2-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-2−2i2i2-2−2i2i000022-2-2−2i−2i2i2i0000000000000000-22-222i−2i2i−2i0000-222i−2i0000000000000000000000000000
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χ9244-4-4-44-444i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000−222222−22−2i22i22i2−2i2000000000000000000000000000000000000
χ9344-4-4-44-44−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000022−22−2222−2i22i22i2−2i2000000000000000000000000000000000000
χ9444-4-4-44-44−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000−222222−222i2−2i2−2i22i2000000000000000000000000000000000000
χ954-44-44-4-444i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000002i2−2i2−2i22i222−22−222200000000000000000000000000000000000000000000
χ964-44-44-4-444i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000000000000000000000000000
χ974-44-44-4-44−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000000000000000000000000000
χ984-44-44-4-44−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000−2i22i22i2−2i222−22−222200000000000000000000000000000000000000000000
χ994-44-4-444-44i−4i4i−4i−4i4i−4i4i00000000-44−4i4i4-44i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-4-444-4−4i4i−4i4i4i−4i4i−4i00000000-444i−4i4-4−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-4444-4-444-4-4-4-4444-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-4444-4-444-4-4-4-444-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4444-4-4-4-44444-4-44-4-44-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4444-4-4-4-44444-4-4-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000

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