Finite Group Databasebeta

← Group #156152

Character table — Group #156152

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111111111111111111111444444444444444444444444888888888888888888888888888888888888888888888888
order12222222222222222222222222222222444444444444444444444444444444444444444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ911111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ1111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1211111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ17111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−i11-1-111-1-1ii−i−iii−i−iii−i−i
χ18111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii-1-111-1-111−i−iii−i−iii−i−iii
χ19111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii11-1-111-1-1ii−i−i-1-111-1-111ii−i−i−i−iii−i−iii
χ20111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii-1-111-1-111−i−iii11-1-111-1-1−i−iiiii−i−iii−i−i
χ21111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii11-1-111-1-1−i−iii−i−iii−i−iii
χ22111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−i-1-111-1-111ii−i−iii−i−iii−i−i
χ23111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i11-1-111-1-1−i−iii-1-111-1-111−i−iiiii−i−iii−i−i
χ24111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i-1-111-1-111ii−i−i11-1-111-1-1ii−i−i−i−iii−i−iii
χ25111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i11-1-1-1-111−i−iiiii−i−i−i−iii
χ26111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii-1-11111-1-1−i−iii-1-11111-1-1ii−i−i−i−iiiii−i−i
χ27111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i11-1-1-1-111ii−i−i-1-11111-1-1−i−iii−i−iiiii−i−i
χ28111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i-1-11111-1-1−i−iii11-1-1-1-111ii−i−iii−i−i−i−iii
χ29111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i11-1-1-1-111−i−iii11-1-1-1-111ii−i−i−i−iiiii−i−i
χ30111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i-1-11111-1-1ii−i−i-1-11111-1-1−i−iiiii−i−i−i−iii
χ31111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii11-1-1-1-111−i−iii-1-11111-1-1ii−i−iii−i−i−i−iii
χ32111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii-1-11111-1-1ii−i−i11-1-1-1-111−i−iii−i−iiiii−i−i
χ3322222-2-2-2-222222-2-2-2-2-2222-2-2-2-222-2-22-2000000000000000022-2-222-2-2000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ3422222-2-2-2-222222-2-2-2-2-2222-2-2-2-222-2-22-2000000000000000022-2-222-2-200000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ3522222-2-2-2-222222-2-2-2-2-2222-2-2-2-222-2-22-20000000000000000-2-222-2-222000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ3622222-2-2-2-222222-2-2-2-2-2222-2-2-2-222-2-22-20000000000000000-2-222-2-22200000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ3722222-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-222-2200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000002i−2i−2i2i-222-200000000000000000000
χ3822222-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-222-2200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000−2i2i2i−2i2-2-2200000000000000000000
χ3922222-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-222-220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000002i−2i−2i2i2-2-2200000000000000000000
χ4022222-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-222-220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000−2i2i2i−2i-222-200000000000000000000
χ41222-2-222-2-2222-2-222-2-2-22-2-222-2-22-22-2-22000000002i2i−2i−2i2i2i−2i−2i000000002i−2i2i−2i00002-22-2000000000000000000000000000000000000
χ42222-2-222-2-2222-2-222-2-2-22-2-222-2-22-22-2-22000000002i2i−2i−2i2i2i−2i−2i00000000−2i2i−2i2i0000-22-22000000000000000000000000000000000000
χ43222-2-222-2-2222-2-222-2-2-22-2-222-2-22-22-2-2200000000−2i−2i2i2i−2i−2i2i2i000000002i−2i2i−2i0000-22-22000000000000000000000000000000000000
χ44222-2-222-2-2222-2-222-2-2-22-2-222-2-22-22-2-2200000000−2i−2i2i2i−2i−2i2i2i00000000−2i2i−2i2i00002-22-2000000000000000000000000000000000000
χ45222-2-222-2-2-2-2-222-2-22222-2-222-2-2-22-222-20000000022-2-2-2-222000000002i−2i−2i2i0000−2i2i2i−2i000000000000000000000000000000000000
χ46222-2-222-2-2-2-2-222-2-22222-2-222-2-2-22-222-20000000022-2-2-2-22200000000−2i2i2i−2i00002i−2i−2i2i000000000000000000000000000000000000
χ47222-2-222-2-2-2-2-222-2-22222-2-222-2-2-22-222-200000000-2-22222-2-2000000002i−2i−2i2i00002i−2i−2i2i000000000000000000000000000000000000
χ48222-2-222-2-2-2-2-222-2-22222-2-222-2-2-22-222-200000000-2-22222-2-200000000−2i2i2i−2i0000−2i2i2i−2i000000000000000000000000000000000000
χ4922-22-22-22-222-22-2-2-222-2-22-22-22-2-222-2-222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000000000002-22-22i−2i2i−2i
χ5022-22-22-22-222-22-2-2-222-2-22-22-22-2-222-2-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000-22-22−2i2i−2i2i
χ5122-22-22-22-222-22-2-2-222-2-22-22-22-2-222-2-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000000000002-22-2−2i2i−2i2i
χ5222-22-22-22-222-22-2-2-222-2-22-22-22-2-222-2-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000-22-222i−2i2i−2i
χ5322-22-22-22-2-2-22-2222-2-22-22-22-22-22-2-222-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000000000002i−2i−2i2i-222-2
χ5422-22-22-22-2-2-22-2222-2-22-22-22-22-22-2-222-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000−2i2i2i−2i2-2-22
χ5522-22-22-22-2-2-22-2222-2-22-22-22-22-22-2-222-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000000000002i−2i−2i2i2-2-22
χ5622-22-22-22-2-2-22-2222-2-22-22-22-22-22-2-222-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000−2i2i2i−2i-222-2
χ572-22-2-2-22222-222-22-22-2-2-2222-2-2-2-2-2222-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000002-22-22i−2i2i−2i000000000000
χ582-22-2-2-22222-222-22-22-2-2-2222-2-2-2-2-2222-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000-22-22−2i2i−2i2i000000000000
χ592-22-2-2-22222-222-22-22-2-2-2222-2-2-2-2-2222-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000002-22-2−2i2i−2i2i000000000000
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χ642-22-2-2-2222-22-2-22-22-222-2222-2-2-222-2-2-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000-222-22i−2i−2i2i000000000000
χ652-2-22-2-2-2-222-2-2-2-2-22-22-22-22222-222222-2000000002-22-22-22-20000000000002-22-200002-22-200000000000000000000000000000000
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χ702-2-22-2-2-2-22-222222-22-222-22222-2-2-2-2-2-22000000002i−2i2i−2i−2i2i−2i2i000000000000-222-20000−2i2i2i−2i00000000000000000000000000000000
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χ812-2-2-22-2-22-22-2-222-222-2222-222-222-22-2-2-22-2-222-2-222i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000
χ822-2-2-22-2-22-22-2-222-222-2222-222-222-22-2-2-22-2-222-2-22−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ832-2-2-22-2-22-22-2-222-222-2222-222-222-22-2-2-2-222-2-222-22i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000
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χ974-44444-4444-44-44-444-4-4-4-4-4-44-4-4-44-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ984-44444-444-44-44-44-4-444-4-4-4-44-4-44-44-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ994-4444-44-4-44-44-444-4-444-4-4-44-444-444-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-4444-44-4-4-44-44-4-444-4-4-4-4-44-4444-4-4444000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-44-4-44-4-4-44-444-4-44-444-444-4444-4-4-4-444000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-44-4-44-4-4-4-44-4-444-44-4-4-444-44444444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-44-4444-44-4-4-4-44-44-444-44-4-4-4444-4-444000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-4444-4-44444-44-44-44-44-4-4-44-4-444-4-4000000000000000000000000000000000000000000000000000000000000000000000000

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