Finite Group Databasebeta

← Group #227021

Character table — Group #227021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888844444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ101111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ171-1-1-111-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-111-1-1-11ii−i−iii−i−i1111-1-1-1-1i−ii−i1-11-111-1-111-1-1ii−i−iii−i−ii−ii−i1-11-1
χ181-1-1-111-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i−i−iii11-1-1-1-111-11ii−i−iii−i−i1111-1-1-1-1i−i−ii1-1-1111-1-1-1-111ii−i−i−i−iii−ii−ii-11-11
χ191-1-1-111-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iiiii−i−i-1-11111-1-1-11ii−i−iii−i−i1111-1-1-1-1−iii−i-111-1-1-11111-1-1−i−iiiii−i−i−ii−ii-11-11
χ201-1-1-111-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-1-111-11ii−i−iii−i−i1111-1-1-1-1−ii−ii-11-11-1-111-1-111−i−iii−i−iiii−ii−i1-11-1
χ211-1-1-111-1111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−iii−i−i11-1-1-1-111-11ii−i−i−i−iii-1-1-1-11111i−ii−i1-1-11-1-11111-1-1−i−iii−i−iiii−i−ii1-1-11
χ221-1-1-111-1111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-111-1-1-11ii−i−i−i−iii-1-1-1-11111i−i−ii1-11-1-1-111-1-111−i−iiiii−i−i−iii−i-111-1
χ231-1-1-111-1111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-111-1-111-11ii−i−i−i−iii-1-1-1-11111−iii−i-11-1111-1-111-1-1ii−i−i−i−iii−iii−i-111-1
χ241-1-1-111-1111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iii−i−iii-1-11111-1-1-11ii−i−i−i−iii-1-1-1-11111−ii−ii-111-111-1-1-1-111ii−i−iii−i−ii−i−ii1-1-11
χ251-1-1-111-1111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−iii−i−i-1-11111-1-1-11−i−iiiii−i−i-1-1-1-11111i−ii−i-111-111-1-1-1-111−i−iii−i−iii−iii−i1-1-11
χ261-1-1-111-1111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-111-1-111-11−i−iiiii−i−i-1-1-1-11111i−i−ii-11-1111-1-111-1-1−i−iiiii−i−ii−i−ii-111-1
χ271-1-1-111-1111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i11-1-111-1-1-11−i−iiiii−i−i-1-1-1-11111−iii−i1-11-1-1-111-1-111ii−i−i−i−iiii−i−ii-111-1
χ281-1-1-111-1111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iii−i−iii11-1-1-1-111-11−i−iiiii−i−i-1-1-1-11111−ii−ii1-1-11-1-11111-1-1ii−i−iii−i−i−iii−i1-1-11
χ291-1-1-111-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111-1-111-11−i−iii−i−iii1111-1-1-1-1i−ii−i-11-11-1-111-1-111ii−i−iii−i−i−ii−ii1-11-1
χ301-1-1-111-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−iii-1-11111-1-1-11−i−iii−i−iii1111-1-1-1-1i−i−ii-111-1-1-11111-1-1ii−i−i−i−iiii−ii−i-11-11
χ311-1-1-111-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iiiii−i−i11-1-1-1-111-11−i−iii−i−iii1111-1-1-1-1−iii−i1-1-1111-1-1-1-111−i−iiiii−i−ii−ii−i-11-11
χ321-1-1-111-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1-11−i−iii−i−iii1111-1-1-1-1−ii−ii1-11-111-1-111-1-1−i−iii−i−iii−ii−ii1-11-1
χ33222222222-22-22-22-200000000222222220000222200002222-2-20000-2-2-2-20000000000-2-200-2-2000000000000000000000000
χ34222222222-22-22-22-200000000222222220000-2-2-2-20000-2-2-2-2-2-20000-2-2-2-20000000000220022000000000000000000000000
χ35222222222-22-22-22-200000000-2-2-2-2-2-2-2-2000022220000-2-2-2-2-2-2000022220000000000-2-20022000000000000000000000000
χ36222222222-22-22-22-200000000-2-2-2-2-2-2-2-20000-2-2-2-200002222-2-20000222200000000002200-2-2000000000000000000000000
χ3722222222-22-22-22-2222222222000000002222000022220000-2-2-2-2-2-2000000000000-2-200-2-200000000000000000000000000
χ3822222222-22-22-22-222222222200000000-2-2-2-20000-2-2-2-20000-2-2-2-2-2-200000000000022002200000000000000000000000000
χ3922222222-22-22-22-22-2-2-2-2-2-2-2-20000000022220000-2-2-2-20000-2-22222000000000000-2-2002200000000000000000000000000
χ4022222222-22-22-22-22-2-2-2-2-2-2-2-200000000-2-2-2-2000022220000-2-222220000000000002200-2-200000000000000000000000000
χ41222-22-2-2-202020-20-222-2-222-2-222−2−222−2−22-22-200002-22-200000000002−22−222−2−222−2−2000000002−22−200002−22−2000000000000
χ42222-22-2-2-202020-20-222-2-222-2-222−2−222−2−2-22-220000-22-2200000000002−22−222−2−222−2−200000000−22−220000−22−22000000000000
χ43222-22-2-2-202020-20-222-2-222-2-2−2−222−2−2222-22-200002-22-20000000000−22−22−2−222−2−22200000000−22−220000−22−22000000000000
χ44222-22-2-2-202020-20-222-2-222-2-2−2−222−2−222-22-220000-22-220000000000−22−22−2−222−2−222000000002−22−200002−22−2000000000000
χ45222-22-2-2-202020-20-2-2-222-2-22222−2−222−2−22-22-20000-22-2200000000002−22−2−2−222−2−222000000002−22−20000−22−22000000000000
χ46222-22-2-2-202020-20-2-2-222-2-22222−2−222−2−2-22-2200002-22-200000000002−22−2−2−222−2−22200000000−22−2200002−22−2000000000000
χ47222-22-2-2-202020-20-2-2-222-2-222−2−222−2−2222-22-20000-22-220000000000−22−2222−2−222−2−200000000−22−2200002−22−2000000000000
χ48222-22-2-2-202020-20-2-2-222-2-222−2−222−2−222-22-2200002-22-20000000000−22−2222−2−222−2−2000000002−22−20000−22−22000000000000
χ4922-22-22-2-22020-20-202−22−22−22−22-22-22-22-200002-22-200002-22-2002−22−200002−22−22−22−20000000000002−22−200002−22−200000000
χ5022-22-22-2-22020-20-202−22−22−22−22-22-22-22-20000-22-220000-22-22002−22−200002−22−22−22−2000000000000−22−220000−22−2200000000
χ5122-22-22-2-22020-20-202−22−22−22−2-22-22-22-2200002-22-20000-22-22002−22−20000−22−22−22−220000000000002−22−20000−22−2200000000
χ5222-22-22-2-22020-20-202−22−22−22−2-22-22-22-220000-22-2200002-22-2002−22−20000−22−22−22−22000000000000−22−2200002−22−200000000
χ5322-22-22-2-22020-20-20−22−22−22−222-22-22-22-200002-22-200002-22-200−22−220000−22−22−22−22000000000000−22−220000−22−2200000000
χ5422-22-22-2-22020-20-20−22−22−22−222-22-22-22-20000-22-220000-22-2200−22−220000−22−22−22−220000000000002−22−200002−22−200000000
χ5522-22-22-2-22020-20-20−22−22−22−22-22-22-22-2200002-22-20000-22-2200−22−2200002−22−22−22−2000000000000−22−2200002−22−200000000
χ5622-22-22-2-22020-20-20−22−22−22−22-22-22-22-220000-22-2200002-22-200−22−2200002−22−22−22−20000000000002−22−20000−22−2200000000
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χ582-22-2-222-220-20-2020i2−i2i2−i2−i2i2−i2i22i−2i2i−2i−2i2i−2i2i0000−2i2i2i−2i0000-222-200i2−i2−i2i200002−22−2−22−22000000000000−222−20000−i2i2i2−i200000000
χ592-22-2-222-220-20-2020i2−i2i2−i2−i2i2−i2i2−2i2i−2i2i2i−2i2i−2i00002i−2i−2i2i0000-222-200i2−i2−i2i20000−22−222−22−20000000000002−2−220000−i2i2i2−i200000000
χ602-22-2-222-220-20-2020i2−i2i2−i2−i2i2−i2i2−2i2i−2i2i2i−2i2i−2i0000−2i2i2i−2i00002-2-2200i2−i2−i2i20000−22−222−22−2000000000000−222−20000i2−i2−i2i200000000
χ612-22-2-222-220-20-2020−i2i2−i2i2i2−i2i2−i22i−2i2i−2i−2i2i−2i2i00002i−2i−2i2i00002-2-2200−i2i2i2−i20000−22−222−22−2000000000000−222−20000−i2i2i2−i200000000
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χ672-2-222-22-2020-20-2022i2i−2i−2i−2i−2i2i2i−i2−i2i2i2i2i2−i2−i22i−2i−2i2i00002-2-220000000000−i2i2i2−i2−2−22222−2−200000000−222−20000−i2i2i2−i2000000000000
χ682-2-222-22-2020-20-2022i2i−2i−2i−2i−2i2i2i−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i0000-222-20000000000−i2i2i2−i2−2−22222−2−2000000002−2−220000i2−i2−i2i2000000000000
χ692-2-222-22-2020-20-202−2i−2i2i2i2i2i−2i−2ii2i2−i2−i2−i2−i2i2i22i−2i−2i2i0000-222-20000000000i2−i2−i2i2−2−22222−2−2000000002−2−220000−i2i2i2−i2000000000000
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χ722-2-222-22-2020-20-202−2i−2i2i2i2i2i−2i−2i−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i00002-2-220000000000−i2i2i2−i222−2−2−2−222000000002−2−220000−i2i2i2−i2000000000000
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χ802-2-2-222-22-222-2-222-2−2i−2i−2i−2i2i2i2i2i00000000−2i−2i2i2i000022-2-200002-22i2i−2i−2i0000000000002i−2i00-2200000000000000000000000000
χ8144444444-4-4-4-4-4-4-4-40000000000000000000000000000000044000000000000000000000000000000000000000000000000
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χ914-444-4-4-44000000002i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ924-444-4-4-4400000000−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ934-444-4-4-4400000000−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000002-2-22-222-200000000000000000000000000000000
χ944-44-4-444-4-404040-402i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ954-44-4-444-4-404040-40−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ964-4-444-44-40-404040-4000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ974-4-444-44-40-404040-400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ984-4-4-444-44-4-444-4-44400000000000000000000000000000000-44000000000000000000000000000000000000000000000000

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