Finite Group Databasebeta

← Group #231569

Character table — Group #231569

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888844444444888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-111111-1-1-1-11111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111-1-1-1-1111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ101111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111-1-111-1-1
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ171-1-1-1111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−i-1ii−i−iii−i−i111-1-111-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ181-1-1-1111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1ii−i−i−i−iii-1ii−i−i−i−iii111-1-111-1-11111-1-1-1-1i−i−iii−i−iiii−i−iii−i−i−i−iii−i−iii-11-11-11-11
χ191-1-1-1111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1−i−iiiii−i−i-1−i−iiiii−i−i111-1-111-1-11111-1-1-1-1−iii−i−iii−i−i−iii−i−iiiii−i−iii−i−i-11-11-11-11
χ201-1-1-1111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii-1−i−iii−i−iii111-1-111-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ211-1-1-1111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−i-1ii−i−i−i−iii111-1-1-1-111-1-1-1-11111i−i−iii−ii−i−i−iii−i−iiiii−i−i−i−iii-111-11-1-11
χ221-1-1-1111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii-1ii−i−iii−i−i111-1-1-1-111-1-1-1-11111i−ii−ii−i−ii−i−iii−i−iii−i−iiiii−i−i1-1-11-111-1
χ231-1-1-1111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−i-1−i−iii−i−iii111-1-1-1-111-1-1-1-11111−ii−ii−iii−iii−i−iii−i−iii−i−i−i−iii1-1-11-111-1
χ241-1-1-1111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iii-1−i−iiiii−i−i111-1-1-1-111-1-1-1-11111−iii−i−ii−iiii−i−iii−i−i−i−iiiii−i−i-111-11-1-11
χ251-1-1-1111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−i-1−i−iiiii−i−i1-1-11111-1-1-1-1-1-11111−iii−ii−ii−iii−i−i−i−iii−i−iii−i−iii-111-1-111-1
χ261-1-1-1111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii-1−i−iii−i−iii1-1-11111-1-1-1-1-1-11111−ii−iii−i−iiii−i−i−i−iiiii−i−iii−i−i1-1-111-1-11
χ271-1-1-1111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i-1ii−i−iii−i−i1-1-11111-1-1-1-1-1-11111i−ii−i−iii−i−i−iiiii−i−i−i−iii−i−iii1-1-111-1-11
χ281-1-1-1111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii-1ii−i−i−i−iii1-1-11111-1-1-1-1-1-11111i−i−ii−ii−ii−i−iiiii−i−iii−i−iii−i−i-111-1-111-1
χ291-1-1-1111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i-1−i−iii−i−iii1-1-111-1-1111111-1-1-1-1−ii−iii−ii−i−i−iiiii−i−i−i−iiiii−i−i1-11-1-11-11
χ301-1-1-1111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iii-1−i−iiiii−i−i1-1-111-1-1111111-1-1-1-1−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii-11-111-11-1
χ311-1-1-1111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−i-1ii−i−i−i−iii1-1-111-1-1111111-1-1-1-1i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i-11-111-11-1
χ321-1-1-1111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iii-1ii−i−iii−i−i1-1-111-1-1111111-1-1-1-1i−ii−i−ii−iiii−i−i−i−iiiii−i−i−i−iii1-11-1-11-11
χ33222222222-222-2-22-2000000002222222200002222-200002222-20000-2-2-2-20000000000-2-200-2-2000000000000000000000000
χ34222222222-222-2-22-200000000222222220000-2-2-2-2-20000-2-2-2-2-20000-2-2-2-20000000000220022000000000000000000000000
χ35222222222-222-2-22-200000000-2-2-2-2-2-2-2-200002222-20000-2-2-2-2-20000222200000000002200-2-2000000000000000000000000
χ36222222222-222-2-22-200000000-2-2-2-2-2-2-2-20000-2-2-2-2-200002222-2000022220000000000-2-20022000000000000000000000000
χ3722222222-22-2-222-22222222220000000022220000-222220000-2-2-2-2-2000000000000-2-200-2-200000000000000000000000000
χ3822222222-22-2-222-222222222200000000-2-2-2-20000-2-2-2-2-20000-2-2-2-2-200000000000022002200000000000000000000000000
χ3922222222-22-2-222-22-2-2-2-2-2-2-2-20000000022220000-2-2-2-2-20000-222220000000000002200-2-200000000000000000000000000
χ4022222222-22-2-222-22-2-2-2-2-2-2-2-200000000-2-2-2-20000-222220000-22222000000000000-2-2002200000000000000000000000000
χ41222-22-2-2-20-2002-2022i2i−2i−2i2i2i−2i−2i22−2−222−2−22-22-2000002i−2i2i−2i0000000002−22−2i2i2−i2−i2i2i2−i2−i2000000002−22−2i2−i2i2−i20000000000000000
χ42222-22-2-2-20-2002-2022i2i−2i−2i2i2i−2i−2i22−2−222−2−2-22-2200000−2i2i−2i2i0000000002−22−2i2i2−i2−i2i2i2−i2−i200000000−22−22−i2i2−i2i20000000000000000
χ43222-22-2-2-20-2002-2022i2i−2i−2i2i2i−2i−2i−2−222−2−2222-22-2000002i−2i2i−2i000000000−22−22−i2−i2i2i2−i2−i2i2i200000000−22−22−i2i2−i2i20000000000000000
χ44222-22-2-2-20-2002-2022i2i−2i−2i2i2i−2i−2i−2−222−2−222-22-2200000−2i2i−2i2i000000000−22−22−i2−i2i2i2−i2−i2i2i2000000002−22−2i2−i2i2−i20000000000000000
χ45222-22-2-2-20-2002-202−2i−2i2i2i−2i−2i2i2i22−2−222−2−22-22-200000−2i2i−2i2i0000000002−22−2−i2−i2i2i2−i2−i2i2i2000000002−22−2−i2i2−i2i20000000000000000
χ46222-22-2-2-20-2002-202−2i−2i2i2i−2i−2i2i2i22−2−222−2−2-22-22000002i−2i2i−2i0000000002−22−2−i2−i2i2i2−i2−i2i2i200000000−22−22i2−i2i2−i20000000000000000
χ47222-22-2-2-20-2002-202−2i−2i2i2i−2i−2i2i2i−2−222−2−2222-22-200000−2i2i−2i2i000000000−22−22i2i2−i2−i2i2i2−i2−i200000000−22−22i2−i2i2−i20000000000000000
χ48222-22-2-2-20-2002-202−2i−2i2i2i−2i−2i2i2i−2−222−2−222-22-22000002i−2i2i−2i000000000−22−22i2i2−i2−i2i2i2−i2−i2000000002−22−2−i2i2−i2i20000000000000000
χ4922-22-22-2-2-202-200202−22−22−22−22i−2i2i−2i2i−2i2i−2i00002-22-2000002i−2i2i−2i02−22−20000i2−i2i2−i2i2−i2i2−i200000000000000002−22−2i2−i2i2−i200000000
χ5022-22-22-2-2-202-200202−22−22−22−22i−2i2i−2i2i−2i2i−2i0000-22-2200000−2i2i−2i2i02−22−20000i2−i2i2−i2i2−i2i2−i20000000000000000−22−22−i2i2−i2i200000000
χ5122-22-22-2-2-202-200202−22−22−22−2−2i2i−2i2i−2i2i−2i2i00002-22-200000−2i2i−2i2i02−22−20000−i2i2−i2i2−i2i2−i2i200000000000000002−22−2−i2i2−i2i200000000
χ5222-22-22-2-2-202-200202−22−22−22−2−2i2i−2i2i−2i2i−2i2i0000-22-22000002i−2i2i−2i02−22−20000−i2i2−i2i2−i2i2−i2i20000000000000000−22−22i2−i2i2−i200000000
χ5322-22-22-2-2-202-20020−22−22−22−222i−2i2i−2i2i−2i2i−2i00002-22-2000002i−2i2i−2i0−22−220000−i2i2−i2i2−i2i2−i2i20000000000000000−22−22−i2i2−i2i200000000
χ5422-22-22-2-2-202-20020−22−22−22−222i−2i2i−2i2i−2i2i−2i0000-22-2200000−2i2i−2i2i0−22−220000−i2i2−i2i2−i2i2−i2i200000000000000002−22−2i2−i2i2−i200000000
χ5522-22-22-2-2-202-20020−22−22−22−22−2i2i−2i2i−2i2i−2i2i00002-22-200000−2i2i−2i2i0−22−220000i2−i2i2−i2i2−i2i2−i20000000000000000−22−22i2−i2i2−i200000000
χ5622-22-22-2-2-202-20020−22−22−22−22−2i2i−2i2i−2i2i−2i2i0000-22-22000002i−2i2i−2i0−22−220000i2−i2i2−i2i2−i2i2−i200000000000000002−22−2−i2i2−i2i200000000
χ572-22-2-22-22202-200-202−22−2−22−222i−2i2i−2i−2i2i−2i2i00002i−2i−2i2i00000-222-202−2−220000i2−i2i2−i2−i2i2−i2i20000000000000000i2−i2−i2i2−222−200000000
χ582-22-2-22-22202-200-202−22−2−22−222i−2i2i−2i−2i2i−2i2i0000−2i2i2i−2i000002-2-2202−2−220000i2−i2i2−i2−i2i2−i2i20000000000000000−i2i2i2−i22−2−2200000000
χ592-22-2-22-22202-200-202−22−2−22−22−2i2i−2i2i2i−2i2i−2i00002i−2i−2i2i000002-2-2202−2−220000−i2i2−i2i2i2−i2i2−i20000000000000000i2−i2−i2i22−2−2200000000
χ602-22-2-22-22202-200-202−22−2−22−22−2i2i−2i2i2i−2i2i−2i0000−2i2i2i−2i00000-222-202−2−220000−i2i2−i2i2i2−i2i2−i20000000000000000−i2i2i2−i2−222−200000000
χ612-22-2-22-22202-200-20−22−222−22−22i−2i2i−2i−2i2i−2i2i00002i−2i−2i2i00000-222-20−222−20000−i2i2−i2i2i2−i2i2−i20000000000000000−i2i2i2−i22−2−2200000000
χ622-22-2-22-22202-200-20−22−222−22−22i−2i2i−2i−2i2i−2i2i0000−2i2i2i−2i000002-2-220−222−20000−i2i2−i2i2i2−i2i2−i20000000000000000i2−i2−i2i2−222−200000000
χ632-22-2-22-22202-200-20−22−222−22−2−2i2i−2i2i2i−2i2i−2i00002i−2i−2i2i000002-2-220−222−20000i2−i2i2−i2−i2i2−i2i20000000000000000−i2i2i2−i2−222−200000000
χ642-22-2-22-22202-200-20−22−222−22−2−2i2i−2i2i2i−2i2i−2i0000−2i2i2i−2i00000-222-20−222−20000i2−i2i2−i2−i2i2−i2i20000000000000000i2−i2−i2i22−2−2200000000
χ652-2-222-2-2202002-20-22i2i−2i−2i−2i−2i2i2i22−2−2−2−2222i−2i−2i2i00000-222-20000000002−2−22i2i2−i2−i2−i2−i2i2i200000000i2−i2−i2i2−222−20000000000000000
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χ672-2-222-2-2202002-20-22i2i−2i−2i−2i−2i2i2i−2−22222−2−22i−2i−2i2i00000-222-2000000000−222−2−i2−i2i2i2i2i2−i2−i200000000−i2i2i2−i22−2−220000000000000000
χ682-2-222-2-2202002-20-22i2i−2i−2i−2i−2i2i2i−2−22222−2−2−2i2i2i−2i000002-2-22000000000−222−2−i2−i2i2i2i2i2−i2−i200000000i2−i2−i2i2−222−20000000000000000
χ692-2-222-2-2202002-20-2−2i−2i2i2i2i2i−2i−2i22−2−2−2−2222i−2i−2i2i000002-2-220000000002−2−22−i2−i2i2i2i2i2−i2−i200000000i2−i2−i2i22−2−220000000000000000
χ702-2-222-2-2202002-20-2−2i−2i2i2i2i2i−2i−2i22−2−2−2−222−2i2i2i−2i00000-222-20000000002−2−22−i2−i2i2i2i2i2−i2−i200000000−i2i2i2−i2−222−20000000000000000
χ712-2-222-2-2202002-20-2−2i−2i2i2i2i2i−2i−2i−2−22222−2−22i−2i−2i2i000002-2-22000000000−222−2i2i2−i2−i2−i2−i2i2i200000000−i2i2i2−i2−222−20000000000000000
χ722-2-222-2-2202002-20-2−2i−2i2i2i2i2i−2i−2i−2−22222−2−2−2i2i2i−2i00000-222-2000000000−222−2i2i2−i2−i2−i2−i2i2i200000000i2−i2−i2i22−2−220000000000000000
χ732-2-2-2222-22-2-2-2222-22222-2-2-2-2000000002i2i−2i−2i000022i2i−2i−2i0000-2-2-222000000000000−2i2i00−2i2i00000000000000000000000000
χ742-2-2-2222-22-2-2-2222-22222-2-2-2-200000000−2i−2i2i2i00002−2i−2i2i2i0000-2-2-2220000000000002i−2i002i−2i00000000000000000000000000
χ752-2-2-2222-22-2-2-2222-2-2-2-2-22222000000002i2i−2i−2i00002−2i−2i2i2i0000-222-2-20000000000002i−2i00−2i2i00000000000000000000000000
χ762-2-2-2222-22-2-2-2222-2-2-2-2-2222200000000−2i−2i2i2i000022i2i−2i−2i0000-222-2-2000000000000−2i2i002i−2i00000000000000000000000000
χ772-2-2-2222-2-2222-2-2-22000000002222-2-2-2-200002i2i−2i−2i200002i2i−2i−2i-20000-2-2220000000000−2i2i00−2i2i000000000000000000000000
χ782-2-2-2222-2-2222-2-2-22000000002222-2-2-2-20000−2i−2i2i2i20000−2i−2i2i2i-20000-2-22200000000002i−2i002i−2i000000000000000000000000
χ792-2-2-2222-2-2222-2-2-2200000000-2-2-2-2222200002i2i−2i−2i20000−2i−2i2i2i-2000022-2-200000000002i−2i00−2i2i000000000000000000000000
χ802-2-2-2222-2-2222-2-2-2200000000-2-2-2-222220000−2i−2i2i2i200002i2i−2i−2i-2000022-2-20000000000−2i2i002i−2i000000000000000000000000
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χ8544-44-44-4-440-4400-40−2222−2222−2222−22220000000000000000000000000022−2222−2200000000000000000000000000000000000000000000
χ8644-4-4-4-444000000002i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000-222-2-222-200000000000000000000000000000000
χ8744-4-4-4-444000000002i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ8844-4-4-4-44400000000−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ8944-4-4-4-44400000000−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000-222-2-222-200000000000000000000000000000000
χ904-444-4-44-4000000002i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ914-444-4-44-4000000002i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000002-2-22-222-200000000000000000000000000000000
χ924-444-4-44-400000000−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000002-2-22-222-200000000000000000000000000000000
χ934-444-4-44-400000000−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ944-44-4-44-44-40-44004022−2222−22−2222−222200000000000000000000000000−222222−2200000000000000000000000000000000000000000000
χ954-44-4-44-44-40-440040−2222−222222−2222−220000000000000000000000000022−22−222200000000000000000000000000000000000000000000
χ964-4-444-4-440-400-4404000000002222−22−22−22−2222220000000000000000000000−222222−220000000000000000000000000000000000000000
χ974-4-444-4-440-400-440400000000−22−2222222222−22−22000000000000000000000022−22−22220000000000000000000000000000000000000000
χ984-4-4-4444-444-4-4-4-444000000000000000000000000-4000000004000000000000000000000000000000000000000000000000

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