Finite Group Databasebeta

← Group #154705

Character table — Group #154705

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111111111111111111111111111444444444444444444444444444444444444444444444444888888888888888888888888888888888888
order12222222222222222222222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1
χ911111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ1111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1211111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ17111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-1
χ18111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i11-1-1−i−iii−i−iii-1-111−i−iii−i−iii-1-111
χ19111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-11111-1-1-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii-1-111
χ20111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−i−i−iii-1-111−i−iiiii−i−i11-1-1−i−iiiii−i−i11-1-1
χ21111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-11111-1-1-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i-1-111
χ22111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iiiii−i−i-1-111ii−i−i−i−iii11-1-1ii−i−i−i−iii11-1-1
χ23111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii11-1-1−i−iii−i−iii11-1-1−i−iii−i−iii11-1-1
χ24111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iii11-1-1ii−i−iii−i−i-1-111ii−i−iii−i−i-1-111
χ25111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iii-1-111ii−i−iii−i−i11-1-1−i−iii−i−iii-1-111
χ26111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii-1-111−i−iii−i−iii-1-111ii−i−iii−i−i11-1-1
χ27111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i11-1-1ii−i−i−i−iii-1-111−i−iiiii−i−i11-1-1
χ28111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−i11-1-1−i−iiiii−i−i11-1-1ii−i−i−i−iii-1-111
χ29111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iii11-1-1−i−iiiii−i−i-1-111ii−i−i−i−iii11-1-1
χ30111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii11-1-1ii−i−i−i−iii11-1-1−i−iiiii−i−i-1-111
χ31111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−i-1-111−i−iii−i−iii11-1-1ii−i−iii−i−i-1-111
χ32111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−i-1-111ii−i−iii−i−i-1-111−i−iii−i−iii11-1-1
χ3322222222-2-2-2-2222222-2-2-2-2-2-222-2-2-2-2-2-222-2-222-2-20000000022-2-222-2-200000000000000000000000000002-22-20000000000000000000000000000
χ3422222222-2-2-2-2222222-2-2-2-2-2-222-2-2-2-2-2-222-2-222-2-200000000-2-222-2-2220000000000000000000000000000-22-220000000000000000000000000000
χ3522222222-2-2-2-2222222-2-2-2-2-2-222-2-2-2-2-2-2-2-222-2-2220000000022-2-222-2-20000000000000000000000000000-22-220000000000000000000000000000
χ3622222222-2-2-2-2222222-2-2-2-2-2-222-2-2-2-2-2-2-2-222-2-22200000000-2-222-2-22200000000000000000000000000002-22-20000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2-2-2222-2-2-2-2-222222-222-2-2-2-222000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000002i−2i−2i2i0000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-2-2-2222-2-2-2-2-222222-222-2-2-2-22200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000−2i2i2i−2i0000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2222-2-2-2-2-222222-2-2-22222-2-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000−2i2i2i−2i0000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2222-2-2-2-2-222222-2-2-22222-2-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000002i−2i−2i2i0000000000000000000000000000
χ412222-2-2-2-222222222-2-222-2-2-2-2-2-222-2-2-2-22-22-22-22-222-2-222-2-2000000000000000000000000000000002-22-200000000000000000000000000000000
χ422222-2-2-2-222222222-2-222-2-2-2-2-2-222-2-2-2-22-22-22-22-2-2-222-2-22200000000000000000000000000000000-22-2200000000000000000000000000000000
χ432222-2-2-2-222222222-2-222-2-2-2-2-2-222-2-2-2-2-22-22-22-2222-2-222-2-200000000000000000000000000000000-22-2200000000000000000000000000000000
χ442222-2-2-2-222222222-2-222-2-2-2-2-2-222-2-2-2-2-22-22-22-22-2-222-2-222000000000000000000000000000000002-22-200000000000000000000000000000000
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χ462222-2-2-2-22222-2-2-2-222-2-22-2-2-222-2-2222-22-22-2-22-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ472222-2-2-2-22222-2-2-2-222-2-22-2-2-222-2-2222-2-22-222-22-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ482222-2-2-2-22222-2-2-2-222-2-22-2-2-222-2-2222-2-22-222-22-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000002i−2i−2i2i00000000000000000000000000000000
χ492222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222222-2-222-2-22000000000000000022-2-222-2-20000000000000000000000002-22-2000000000000000000000000
χ502222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222222-2-222-2-220000000000000000-2-222-2-222000000000000000000000000-22-22000000000000000000000000
χ512222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-222-2-222-2000000000000000022-2-222-2-2000000000000000000000000-22-22000000000000000000000000
χ522222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-222-2-222-20000000000000000-2-222-2-2220000000000000000000000002-22-2000000000000000000000000
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χ542222-2-2-2-2-2-2-2-2-2-2-2-22222-22222222-2-2-222-2-22-222-20000000000000000-2-22222-2-2000000000000000000000000-222-2000000000000000000000000
χ552222-2-2-2-2-2-2-2-2-2-2-2-22222-22222222-2-2-22-222-22-2-22000000000000000022-2-2-2-222000000000000000000000000-222-2000000000000000000000000
χ562222-2-2-2-2-2-2-2-2-2-2-2-22222-22222222-2-2-22-222-22-2-220000000000000000-2-22222-2-20000000000000000000000002-2-22000000000000000000000000
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χ5822-2-222-2-222-2-222-2-2222-222-2-2-2-22-22-2-2200000000000000002i−2i2i−2i2i−2i2i−2i00000000-2-222-2-222000000000000000000000000−2i2i−2i2i0000000000000000
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χ852-22-2-22-222-22-2-22-222-2-2-222-222-222-22-2-2000000002-2-22-222-200000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000−2i2i2i−2i00000000000000000000
χ862-22-2-22-222-22-2-22-222-2-2-222-222-222-22-2-2000000002-2-22-222-20000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000002i−2i−2i2i00000000000000000000
χ872-22-2-22-222-22-2-22-222-2-2-222-222-222-22-2-200000000-222-22-2-2200000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000002i−2i−2i2i00000000000000000000
χ882-22-2-22-222-22-2-22-222-2-2-222-222-222-22-2-200000000-222-22-2-220000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000−2i2i2i−2i00000000000000000000
χ892-2-222-2-22-222-22-2-222-2-22-222-2-222-222-2-20000000000000000000000002-22-22-22-2000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000002i−2i2i−2i
χ902-2-222-2-22-222-22-2-222-2-22-222-2-222-222-2-20000000000000000000000002-22-22-22-200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000−2i2i−2i2i
χ912-2-222-2-22-222-22-2-222-2-22-222-2-222-222-2-2000000000000000000000000-22-22-22-22000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000−2i2i−2i2i
χ922-2-222-2-22-222-22-2-222-2-22-222-2-222-222-2-2000000000000000000000000-22-22-22-2200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000002i−2i2i−2i
χ932-2-222-2-22-222-2-222-2-222-2222-22-2-22-2-22-20000000000000000000000002-22-2-22-22000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000002i−2i−2i2i
χ942-2-222-2-22-222-2-222-2-222-2222-22-2-22-2-22-20000000000000000000000002-22-2-22-2200000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000−2i2i2i−2i
χ952-2-222-2-22-222-2-222-2-222-2222-22-2-22-2-22-2000000000000000000000000-22-222-22-2000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000−2i2i2i−2i
χ962-2-222-2-22-222-2-222-2-222-2222-22-2-22-2-22-2000000000000000000000000-22-222-22-200000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000002i−2i−2i2i
χ972-2-22-222-22-2-222-2-22-222-2-222-22-2-2222-2-20000000000000000000000002-2-222-2-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000002i−2i2i−2i000000000000
χ982-2-22-222-22-2-222-2-22-222-2-222-22-2-2222-2-20000000000000000000000002-2-222-2-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000−2i2i−2i2i000000000000
χ992-2-22-222-22-2-222-2-22-222-2-222-22-2-2222-2-2000000000000000000000000-222-2-222-22i−2i−2i2i2i−2i−2i2i0000000000000000000000000000−2i2i−2i2i000000000000
χ1002-2-22-222-22-2-222-2-22-222-2-222-22-2-2222-2-2000000000000000000000000-222-2-222-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000002i−2i2i−2i000000000000
χ1012-2-22-222-22-2-22-222-22-2-22222-2-222-2-2-22-20000000000000000000000002-2-22-222-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000002i−2i−2i2i000000000000
χ1022-2-22-222-22-2-22-222-22-2-22222-2-222-2-2-22-20000000000000000000000002-2-22-222-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000−2i2i2i−2i000000000000
χ1032-2-22-222-22-2-22-222-22-2-22222-2-222-2-2-22-2000000000000000000000000-222-22-2-222i−2i−2i2i−2i2i2i−2i0000000000000000000000000000−2i2i2i−2i000000000000
χ1042-2-22-222-22-2-22-222-22-2-22222-2-222-2-2-22-2000000000000000000000000-222-22-2-22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000002i−2i−2i2i000000000000
χ10544-4-4-4-44444-4-444-4-4-4-44-4-4-444444-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10644-4-4-4-44444-4-4-4-44444-444-444-4-4-444-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10744-4-4-4-444-4-44444-4-4-4-4-4444-4-444-444-4-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10844-4-4-4-444-4-444-4-444444-4-44-4-4-4-44-4-4444000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1094-44-44-44-4-44-444-44-44-4-4-4-44-444-4444-44-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1104-44-44-44-4-44-44-44-44-444444-44-44-4-4-44-4-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1114-44-4-44-44-44-444-44-4-44-4-44-44-4-4444-44-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1124-44-4-44-44-44-44-44-444-444-4-44-44-4-4-44-444000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1134-4-444-4-444-4-444-4-444-44-44-4-44-44-44-4-444000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1144-4-444-4-444-4-44-444-4-44-44-4-4-444-44-444-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1154-4-44-444-4-444-44-4-44-44-444-4-444-44-4-4-444000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1164-4-44-444-4-444-4-444-44-44-4-4-4-44-44-4444-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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