Finite Group Databasebeta

← Group #110021

Character table — Group #110021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222444444442222444444444444444444444444888888888888888888888888444488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-11iiii−i−i−i−i11111111-1-1-1-1-1-1-1-111-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-11iiii−i−i−i−i-1-1-1-1-1-1-1-11111111111-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-11−i−i−i−iiiii11111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-11−i−i−i−iiiii-1-1-1-1-1-1-1-11111111111-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-111111iiii−i−i−i−i11111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-111111iiii−i−i−i−i-1-1-1-1-1-1-1-111111111-1-111ii−i−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1ii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-111111−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-111111−i−i−i−iiiii-1-1-1-1-1-1-1-111111111-1-111−i−iiiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−i−iii
χ171-1-1111-1-111-1-1-1-11111-1-11111-1-1-111-1-1-1-11-1ii−i−iii−i−i1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1i−ii−ii−ii−i11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ181-1-1111-1-111-1-1-1-11111-1-11111-1-1-111-1-1-1-11-1ii−i−iii−i−i1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111i−ii−ii−ii−i11-1-111-1-1−i−iii−i−iii−i−iii−i−iii-11-11
χ191-1-1111-1-111-1-1-1-11111-1-11111-1-1-111-1-1-1-11-1ii−i−iii−i−i1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1i−ii−i−ii−ii-1-111-1-111−i−iii−i−iiiii−i−iii−i−i-11-11
χ201-1-1111-1-111-1-1-1-11111-1-11111-1-1-111-1-1-1-11-1ii−i−iii−i−i1−i−iii−i−iii-1-1-1-11111-1-1-1-11111i−ii−i−ii−ii-1-111-1-111ii−i−iii−i−i−i−iii−i−iii1-11-1
χ211-1-1111-1-111-1-1-1-11111-1-11111-1-1-111-1-1-1-11-1−i−iii−i−iii1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1−ii−iii−ii−i-1-111-1-111ii−i−iii−i−i−i−iii−i−iii-11-11
χ221-1-1111-1-111-1-1-1-11111-1-11111-1-1-111-1-1-1-11-1−i−iii−i−iii1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111−ii−iii−ii−i-1-111-1-111−i−iii−i−iiiii−i−iii−i−i1-11-1
χ231-1-1111-1-111-1-1-1-11111-1-11111-1-1-111-1-1-1-11-1−i−iii−i−iii1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii11-1-111-1-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ241-1-1111-1-111-1-1-1-11111-1-11111-1-1-111-1-1-1-11-1−i−iii−i−iii1−i−iii−i−iii-1-1-1-11111-1-1-1-11111−ii−ii−ii−ii11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-11-11
χ251-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-1-11ii−i−i−i−iii111-1-1-1-1111111-1-1-1-1-1-1-1-11111i−i−ii1-1-11−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii−iii−i
χ261-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-1-11ii−i−i−i−iii111-1-1-1-111-1-1-1-111111111-1-1-1-1i−i−ii1-1-11−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−ii−i−ii
χ271-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-1-11ii−i−i−i−iii1-1-11111-1-11111-1-1-1-1-1-1-1-11111i−i−ii-111-1ii−i−i−i−iii-1-11111-1-1ii−i−i−i−iiii−i−ii
χ281-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-1-11ii−i−i−i−iii1-1-11111-1-1-1-1-1-111111111-1-1-1-1i−i−ii-111-1ii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i−iii−i
χ291-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-1-11−i−iiiii−i−i111-1-1-1-1111111-1-1-1-1-1-1-1-11111−iii−i1-1-11ii−i−i−i−iii11-1-1-1-111−i−iiiii−i−ii−i−ii
χ301-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-1-11−i−iiiii−i−i111-1-1-1-111-1-1-1-111111111-1-1-1-1−iii−i1-1-11ii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii−iii−i
χ311-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-1-11−i−iiiii−i−i1-1-11111-1-11111-1-1-1-1-1-1-1-11111−iii−i-111-1−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i−iii−i
χ321-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-1-11−i−iiiii−i−i1-1-11111-1-1-1-1-1-111111111-1-1-1-1−iii−i-111-1−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iiii−i−ii
χ332222222222222222222222-2-22-2-2-2-2-2-22-2-2-200000000-22222222200000000000000000000-2-2-2-20000000000000000000000000000
χ342222222222222222222222-2-22-2-2-2-2-2-22-2-2-200000000-2-2-2-2-2-2-2-2-20000000000000000000022220000000000000000000000000000
χ352222222222222222-2-2-2-2-2-222-2222222-2-2-2-222222222-2000000000000000000000000-2-2-2-200000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-222-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000222200000000000000000000000000000000
χ372222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222000000002000000000000000000000000000000002-22-22-22-200000000000000000000
χ382222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222200000000200000000000000000000000000000000-22-22-22-2200000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222-2-222-222-2-2-2-2-2-2222222-2-2-2-2-2000000000000000000000000-2-22200000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-222-222-2-2-2-2-2-222-2-2-2-22222-200000000000000000000000022-2-200000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-22222-22-2-2000000002000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ4222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-22222-22-2-200000000200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22-2-222222-22200000000-22i2i2i2i−2i−2i−2i−2i00000000000000000000−2i−2i2i2i0000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22-2-222222-22200000000-2−2i−2i−2i−2i2i2i2i2i000000000000000000002i2i−2i−2i0000000000000000000000000000
χ452222-2-2-2-22222-2-2-2-22-22-22-2002000000-20000000000002-22-22-22-222−2−222−2−222−2−222−2−200000000000000002−22−22−22−2000000000000
χ462222-2-2-2-22222-2-2-2-22-22-22-2002000000-20000000000002-22-22-22-2−2−222−2−222−2−222−2−2220000000000000000−22−22−22−22000000000000
χ472222-2-2-2-22222-2-2-2-22-22-22-2002000000-2000000000000-22-22-22-2222−2−222−2−222−2−222−2−20000000000000000−22−22−22−22000000000000
χ482222-2-2-2-22222-2-2-2-22-22-22-2002000000-2000000000000-22-22-22-22−2−222−2−222−2−222−2−22200000000000000002−22−22−22−2000000000000
χ492222-2-2-2-2-2-2-2-22222-22-222-2002000000-20000000000002i−2i2i−2i−2i2i−2i2i22−2−222−2−2−2−222−2−2220000000000000000i2−i2i2−i2−i2i2−i2i2000000000000
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χ522222-2-2-2-2-2-2-2-22222-22-222-2002000000-2000000000000−2i2i−2i2i2i−2i2i−2i−2−222−2−22222−2−222−2−20000000000000000i2−i2i2−i2−i2i2−i2i2000000000000
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χ5422-2-22-22-22i−2i2i−2i2i−2i2i−2i0000002-202-22i−2i2i−2i00002-22-22i−2i2i−2i000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000000000000000−i2i2−i2i2−22−220000
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χ702-2-2222-2-222-2-2-2-22222-2-222-2-2-222-2-222-22-2200000000-2−2i−2i2i2i−2i−2i2i2i000000000000000000002i−2i2i−2i0000000000000000000000000000
χ712-2-2222-2-222-2-2-2-222-2-222-2-2222-2-222-2-222-222i2i−2i−2i2i2i−2i−2i-2000000000000000000000000−2i2i−2i2i00000000000000000000000000000000
χ722-2-2222-2-222-2-2-2-222-2-222-2-2222-2-222-2-222-22−2i−2i2i2i−2i−2i2i2i-20000000000000000000000002i−2i2i−2i00000000000000000000000000000000
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χ762-2-2222-2-2-2-22222-2-222-2-2-2-2222-2-2-2-222222-2−2i−2i2i2i2i2i−2i−2i-20000000000000000000000002i−2i−2i2i00000000000000000000000000000000
χ772-2-2222-2-2-2-22222-2-222-2-2-2-2-2-222222-2-22-2-22000000002000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ782-2-2222-2-2-2-22222-2-222-2-2-2-2-2-222222-2-22-2-2200000000200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ792-2-2222-2-2-2-22222-2-2-2-22222-2-2-22222-2-2-222-200000000-222-2-2-2-22200000000000000000000-222-20000000000000000000000000000
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χ812-2-22-2-22222-2-222-2-22-2-222-200-200000020000000000002i−2i−2i2i2i−2i−2i2i22−2−2−2−22222−2−2−2−2220000000000000000i2−i2−i2i2i2−i2−i2i2000000000000
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χ832-2-22-2-22222-2-222-2-22-2-222-200-20000002000000000000−2i2i2i−2i−2i2i2i−2i22−2−2−2−22222−2−2−2−2220000000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ842-2-22-2-22222-2-222-2-22-2-222-200-20000002000000000000−2i2i2i−2i−2i2i2i−2i−2−22222−2−2−2−22222−2−20000000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ852-2-22-2-222-2-222-2-222-222-22-200-200000020000000000002-2-22-222-222−2−2−2−222−2−22222−2−200000000000000002−2−22−222−2000000000000
χ862-2-22-2-222-2-222-2-222-222-22-200-200000020000000000002-2-22-222-2−2−22222−2−222−2−2−2−2220000000000000000−222−22−2−22000000000000
χ872-2-22-2-222-2-222-2-222-222-22-200-20000002000000000000-222-22-2-2222−2−2−2−222−2−22222−2−20000000000000000−222−22−2−22000000000000
χ882-2-22-2-222-2-222-2-222-222-22-200-20000002000000000000-222-22-2-22−2−22222−2−222−2−2−2−22200000000000000002−2−22−222−2000000000000
χ894444-4-4-4-44444-4-4-4-4-44-44-4400-40000004000000000000000000000000000000000000000000000000000000000000000000000000
χ904444-4-4-4-4-4-4-4-444444-44-4-4400-40000004000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-44-44-44i−4i4i−4i4i−4i4i−4i000000-440-44−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000
χ9244-4-44-44-4−4i4i−4i4i−4i4i−4i4i000000-440-444i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000
χ9344-4-4-44-444i−4i4i−4i−4i4i−4i4i0000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i2-2-222-2-22000000000000000000000000000000000000
χ9444-4-4-44-444i−4i4i−4i−4i4i−4i4i000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i-222-2-222-2000000000000000000000000000000000000
χ9544-4-4-44-44−4i4i−4i4i4i−4i4i−4i0000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i-222-2-222-2000000000000000000000000000000000000
χ9644-4-4-44-44−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i2-2-222-2-22000000000000000000000000000000000000
χ974-44-44-4-444i−4i−4i4i−4i4i4i−4i000000-4404-4−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000
χ984-44-44-4-44−4i4i4i−4i4i−4i−4i4i000000-4404-44i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000
χ994-44-4-444-44i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i2-2-22-222-2000000000000000000000000000000000000
χ1004-44-4-444-44i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i-222-22-2-22000000000000000000000000000000000000
χ1014-44-4-444-4−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i-222-22-2-22000000000000000000000000000000000000
χ1024-44-4-444-4−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i2-2-22-222-2000000000000000000000000000000000000
χ1034-4-44-4-44444-4-444-4-4-444-4-44004000000-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-4-444-4-444-4-4444-4-44-44004000000-4000000000000000000000000000000000000000000000000000000000000000000000000

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