Finite Group Databasebeta

← Group #359244

Character table — Group #359244

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222222222224444444444444444444444448888888888888888224444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111
χ911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ17111-1-111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ18111-1-111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−i-1-111−i−iii-1-111−i−iii-1-111−i−iii-1-111−i−iii11-1-1ii−i−i
χ19111-1-111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1iiii−i−i−i−i-11-11−i−iii11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii-1-111−i−iii
χ20111-1-111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1iiii−i−i−i−i-11-11−i−iii-1-111−i−iii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii
χ21111-1-111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-1-11111−i−i−i−iiiii1-11-1ii−i−i11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii-1-111−i−iii
χ22111-1-111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-1-11111−i−i−i−iiiii1-11-1ii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii
χ23111-1-111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-1-11111−i−i−i−iiiii-11-11−i−iii11-1-1ii−i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i
χ24111-1-111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-1-11111−i−i−i−iiiii-11-11−i−iii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i
χ25111-1-111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii
χ26111-1-111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii
χ27111-1-111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1−i−i−i−iiiii-11-11ii−i−i11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i
χ28111-1-111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1−i−i−i−iiiii-11-11ii−i−i-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i
χ29111-1-111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-1-11111iiii−i−i−i−i1-11-1−i−iii11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i
χ30111-1-111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-1-11111iiii−i−i−i−i1-11-1−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i
χ31111-1-111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-1-11111iiii−i−i−i−i-11-11ii−i−i11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii
χ32111-1-111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-1-11111iiii−i−i−i−i-11-11ii−i−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii
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χ342222222222222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000-2-222-22-220000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000022-2-2-22-220000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000-2-2222-22-20000000000000000000000000000000000000000
χ37222-2-222222-2-2-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-2-22200000000000000002-2-222i−2i−2i2i0000000000000000000000000000000000000000
χ38222-2-222222-2-2-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-2-2220000000000000000-222-2−2i2i2i−2i0000000000000000000000000000000000000000
χ39222-2-222222-2-2-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-2-22200000000000000002-2-22−2i2i2i−2i0000000000000000000000000000000000000000
χ40222-2-222222-2-2-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-2-2220000000000000000-222-22i−2i−2i2i0000000000000000000000000000000000000000
χ4122-22-222-2-2-2222-2-2-22-22-222-2-222-2-222-2-222-2-22-22-20000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
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χ4622-22-222-2-2-2222-2-2-2-22-2222-2-2-2-22222-2-2-2-222-22-2200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
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χ4822-22-222-2-2-2222-2-2-2-22-22-2-22222-2-2-2-22222-2-2-22-2200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4922-2-2222-2-2-2-2-2-22222-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2-2-220000000000000000000000000000000000000000000000002i−2i−2i2i-222-200000000
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χ5422-2-2222-2-2-2-2-2-2222-222-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-222-200000000000000000000000000000000−2i2i2i−2i2-2-22000000000000000000000000
χ5522-2-2222-2-2-2-2-2-2222-222-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-222-2000000000000000000000000000000002i−2i−2i2i2-2-22000000000000000000000000
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χ582-222-22-22-2-22-2-222-22-2-222i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i-222-2000000000000000000000000−2i2i−2i2i-22-2200000000000000000000000000000000
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χ602-222-22-22-2-22-2-222-22-2-22−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i-222-2000000000000000000000000−2i2i−2i2i2-22-200000000000000000000000000000000
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χ742-2-2222-2-2222-2-2-2-2222-2-22i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i-2-22200000000000000000000000000000000000000000000000000000000−2i2i−2i2i-22-22
χ752-2-2222-2-2222-2-2-2-2222-2-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i-2-222000000000000000000000000000000000000000000000000000000002i−2i2i−2i-22-22
χ762-2-2222-2-2222-2-2-2-2222-2-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i-2-22200000000000000000000000000000000000000000000000000000000−2i2i−2i2i2-22-2
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χ8944444-4-4-44-4-44-44-4-40000000000000000000000000000000022−2222−2222−2222−22000000000000000000000000000000000000000000000000
χ9044444-4-4-44-4-44-44-4-400000000000000000000000000000000−2222−2222−2222−2222000000000000000000000000000000000000000000000000
χ91444-4-4-4-4-44-44-44-444000000000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ92444-4-4-4-4-44-44-44-44400000000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ9344-44-4-4-44-44-44-4-4440000000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000000000000000000000
χ9444-44-4-4-44-44-44-4-444000000000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000000000000000000000
χ9544-4-44-4-44-444-444-4-40000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000000000000000000000
χ9644-4-44-4-44-444-444-4-4000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000000000000000000000
χ974-444-4-44-4-44-4-444-440000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000000000000000
χ984-444-4-44-4-44-4-444-44000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000000000000000
χ994-44-44-44-4-4444-4-44-40000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000000000000000000000
χ1004-44-44-44-4-4444-4-44-4000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000000000000000000000
χ1014-4-444-4444-4-4-44-44-4000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ1024-4-444-4444-4-4-44-44-400000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ1034-4-4-4-4-4444-444-44-440000000000000000000000000000000022−22−2222−222222−22000000000000000000000000000000000000000000000000
χ1044-4-4-4-4-4444-444-44-4400000000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000000000000000000000

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