Finite Group Databasebeta

← Group #188293

Character table — Group #188293

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222222222222444444444444444444444444444444444444444444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ17111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11-11-11-11-11-11-1
χ18111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11-11-11-11-11
χ19111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-11-11-1-11-11-11-11
χ20111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-11-111-11-11-11-1
χ21111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111i−ii−i−ii−iii−ii−i−ii−ii
χ22111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111−ii−iii−ii−i−ii−iii−ii−i
χ23111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1i−ii−i−ii−ii−ii−iii−ii−i
χ24111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1−ii−iii−ii−ii−ii−i−ii−ii
χ25111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-1-111-1-111-1-11
χ26111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-111-1-111-1-111-1
χ27111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-111-1-11-111-1-111-1
χ28111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-111-11-1-111-1-11
χ29111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1i−i−ii−iii−ii−i−ii−iii−i
χ30111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−iii−ii−i−ii−iii−ii−i−ii
χ31111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111i−i−ii−iii−i−iii−ii−i−ii
χ32111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−iii−ii−i−iii−i−ii−iii−i
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χ3722222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2222222-2-222-2-20000000000000000-2-22222-2-2-2-22200000000000000000000000000000000
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χ3922222222-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-222-2-222-2-20000000000000000-2-222-2-22222-2-200000000000000000000000000000000
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χ842-2-2222-2-2-222-20000000022-2-2-2-22200000000−2i2i2i−2i2i−2i−2i2i-222-20000-222-200000000−2i2i2i−2i00002i−2i−2i2i0000−2i2i2i−2i00000000000000000000
χ852-2-2222-2-2-222-200000000-2-22222-2-2000000002i−2i−2i2i−2i2i2i−2i2-2-220000-222-200000000−2i2i2i−2i00002i−2i−2i2i00002i−2i−2i2i00000000000000000000
χ862-2-2222-2-2-222-200000000-2-22222-2-2000000002i−2i−2i2i−2i2i2i−2i-222-200002-2-2200000000−2i2i2i−2i0000−2i2i2i−2i0000−2i2i2i−2i00000000000000000000
χ872-2-2222-2-2-222-200000000-2-22222-2-200000000−2i2i2i−2i2i−2i−2i2i2-2-220000-222-2000000002i−2i−2i2i0000−2i2i2i−2i0000−2i2i2i−2i00000000000000000000
χ882-2-2222-2-2-222-200000000-2-22222-2-200000000−2i2i2i−2i2i−2i−2i2i-222-200002-2-22000000002i−2i−2i2i00002i−2i−2i2i00002i−2i−2i2i00000000000000000000
χ89444-44-4-4-4000000004-44-400004-44-44-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ90444-44-4-4-4000000004-44-40000-44-44-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ91444-44-4-4-400000000-44-4400004-44-4-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ92444-44-4-4-400000000-44-440000-44-444-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9344-4-4-44-4400004-44-400004i−4i4i−4i00004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9444-4-4-44-4400004-44-40000−4i4i−4i4i0000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9544-4-4-44-440000-44-4400004i−4i4i−4i0000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9644-4-4-44-440000-44-440000−4i4i−4i4i00004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ974-44-4-444-4000000004-4-444i−4i−4i4i000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ984-44-4-444-4000000004-4-44−4i4i4i−4i00000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ994-44-4-444-400000000-444-44i−4i−4i4i00000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-4-444-400000000-444-4−4i4i4i−4i000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-4-44-44400004-4-44000000004-4-4400004-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-4-44-44400004-4-4400000000-444-40000-444-400000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-44-4440000-444-4000000004-4-440000-444-400000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-44-4440000-444-400000000-444-400004-4-4400000000000000000000000000000000000000000000000000000000000000000000

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