Finite Group Databasebeta

← Group #224660

Character table — Group #224660

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11111111222222222222222222224444444444444444444444444444448888888888888888888888888888888161616161616
order12222222444444444444444444444444444444444488888888888888884444444888888888888888888888888444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ71111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-11111111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111111111-11-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111
χ11111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111
χ12111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-111111111-1-1-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ16111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ1711111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-11-11-1
χ1811111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii111-1-111ii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii-11-11-11
χ1911111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i111-1-111−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−i-11-11-11
χ2011111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-11-11-1
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−iiiii−i−i−i−i1-1-111-1-1ii−i−i−i−iii−i−iiiii−i−i−i−iii−i−iii1-1-11-11
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-111ii−i−i−i−iii−i−iii−i−iiiii−i−iii−i−i-111-11-1
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-111−i−iiiii−i−iii−i−iii−i−i−i−iii−i−iii-111-11-1
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiii−i−i−i−iiiii1-1-111-1-1−i−iiiii−i−iii−i−i−i−iiiii−i−iii−i−i1-1-11-11
χ2511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i-11-111-1-1−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iii-111-1-11
χ2611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-11-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-111-1
χ2711111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-11-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii1-1-111-1
χ2811111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii-11-111-1-1ii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i-111-1-11
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1-1111-1-1−i−iii−i−iiiii−i−i−i−iii−i−iiiii−i−i-11-111-1
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11-1-111−i−iii−i−iiiii−i−iii−i−iii−i−i−i−iii1-11-1-11
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11-1-111ii−i−iii−i−i−i−iii−i−iii−i−iiiii−i−i1-11-1-11
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1-1111-1-1ii−i−iii−i−i−i−iiiii−i−iii−i−i−i−iii-11-111-1
χ332222222222-2-22222222222222-22-222-2-222-2-222-2-2-2-20000000000000000-2-2-20000000000000000000000000000000000
χ342222222222-2-22222-2-2-2-2-2-2-2-22-22-222-2-2-2-222-2-222-2-20000000000000000-2220000000000000000000000000000000000
χ352222222222-2-2-2-2-2-22222-2-2-2-22-22-2-2-22222-2-2-2-222-2-200000000000000002-220000000000000000000000000000000000
χ362222222222-2-2-2-2-2-2-2-2-2-222222-22-2-2-222-2-22222-2-2-2-2000000000000000022-20000000000000000000000000000000000
χ3722222222-2-222222222222222-22-22-2-222-2-222-2-222-2-20000000000000000-2-2-20000000000000000000000000000000000
χ3822222222-2-2222222-2-2-2-2-2-2-2-2-22-22-2-22222-2-222-2-2-2-20000000000000000-2220000000000000000000000000000000000
χ3922222222-2-222-2-2-2-22222-2-2-2-2-22-2222-2-2-2-22222-2-2-2-200000000000000002-220000000000000000000000000000000000
χ4022222222-2-222-2-2-2-2-2-2-2-22222-22-2222-2-222-2-2-2-222-2-2000000000000000022-20000000000000000000000000000000000
χ41222-2-2-2-222-22-20000000000002-2-220000000000002-222-2-222-2-22i2i−2i−2i2i2i−2i−2i0002i−2i2i−2i000000000000000000000000000000
χ42222-2-2-2-222-22-20000000000002-2-220000000000002-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i000−2i2i−2i2i000000000000000000000000000000
χ43222-2-2-2-222-22-20000000000002-2-220000000000002-2-2-222-2-2222i2i−2i−2i2i2i−2i−2i000−2i2i−2i2i000000000000000000000000000000
χ44222-2-2-2-222-22-20000000000002-2-220000000000002-2-2-222-2-222−2i−2i2i2i−2i−2i2i2i0002i−2i2i−2i000000000000000000000000000000
χ45222-2-2-2-22-22-22000000000000-222-20000000000002-22i2i−2i−2i−2i−2i2i2i22-2-2-2-222000−2i2i2i−2i000000000000000000000000000000
χ46222-2-2-2-22-22-22000000000000-222-20000000000002-22i2i−2i−2i−2i−2i2i2i-2-22222-2-20002i−2i−2i2i000000000000000000000000000000
χ47222-2-2-2-22-22-22000000000000-222-20000000000002-2−2i−2i2i2i2i2i−2i−2i22-2-2-2-2220002i−2i−2i2i000000000000000000000000000000
χ48222-2-2-2-22-22-22000000000000-222-20000000000002-2−2i−2i2i2i2i2i−2i−2i-2-22222-2-2000−2i2i2i−2i000000000000000000000000000000
χ4922-222-2-2-2002222-2-222-2-222-2-20-20-2002-2002-2002-2002−22−22−22−20000000000000002−22−22−22−22−22−2000000000000000000
χ5022-222-2-2-2002222-2-222-2-222-2-20-20-2002-2002-2002-200−22−22−22−22000000000000000−22−22−22−22−22−22000000000000000000
χ5122-222-2-2-2002222-2-2-2-222-2-2220-20-2002-200-2200-22002−22−22−22−20000000000000002−22−2−22−22−22−22000000000000000000
χ5222-222-2-2-2002222-2-2-2-222-2-2220-20-2002-200-2200-2200−22−22−22−22000000000000000−22−222−22−22−22−2000000000000000000
χ5322-222-2-2-20022-2-22222-2-2-2-2220-20-200-22002-200-22002−22−22−22−2000000000000000−22−222−22−2−22−22000000000000000000
χ5422-222-2-2-20022-2-22222-2-2-2-2220-20-200-22002-200-2200−22−22−22−220000000000000002−22−2−22−222−22−2000000000000000000
χ5522-222-2-2-20022-2-222-2-22222-2-20-20-200-2200-22002-2002−22−22−22−2000000000000000−22−22−22−222−22−2000000000000000000
χ5622-222-2-2-20022-2-222-2-22222-2-20-20-200-2200-22002-200−22−22−22−220000000000000002−22−22−22−2−22−22000000000000000000
χ5722-222-2-2-200-2-222-2-222-2-222-2-2020200-2200-2200-2200i2−i2i2−i2−i2i2−i2i2000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ5822-222-2-2-200-2-222-2-222-2-222-2-2020200-2200-2200-2200−i2i2−i2i2i2−i2i2−i2000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ5922-222-2-2-200-2-222-2-2-2-222-2-222020200-22002-2002-200i2−i2i2−i2−i2i2−i2i2000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ6022-222-2-2-200-2-222-2-2-2-222-2-222020200-22002-2002-200−i2i2−i2i2i2−i2i2−i2000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ6122-222-2-2-200-2-2-2-22222-2-2-2-2220202002-200-22002-200i2−i2i2−i2−i2i2−i2i2000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000000000
χ6222-222-2-2-200-2-2-2-22222-2-2-2-2220202002-200-22002-200−i2i2−i2i2i2−i2i2−i2000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000000000
χ6322-222-2-2-200-2-2-2-222-2-22222-2-20202002-2002-200-2200i2−i2i2−i2−i2i2−i2i2000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000000000
χ6422-222-2-2-200-2-2-2-222-2-22222-2-20202002-2002-200-2200−i2i2−i2i2i2−i2i2−i2000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000000000
χ652-222-22-2-222002-22-22-22-22-22-2-20-202-2002-2002-20000000000002−22−22−22−200000000000000000002−22−22−22−22−22−2000000
χ662-222-22-2-222002-22-22-22-22-22-2-20-202-2002-2002-2000000000000−22−22−22−220000000000000000000−22−22−22−22−22−22000000
χ672-222-22-2-222002-22-2-22-22-22-22-20-202-200-2200-220000000000002−22−22−22−200000000000000000002−22−2−22−22−22−22000000
χ682-222-22-2-222002-22-2-22-22-22-22-20-202-200-2200-22000000000000−22−22−22−220000000000000000000−22−222−22−22−22−2000000
χ692-222-22-2-22200-22-222-22-2-22-22-20-20-22002-200-220000000000002−22−22−22−20000000000000000000−22−222−22−2−22−22000000
χ702-222-22-2-22200-22-222-22-2-22-22-20-20-22002-200-22000000000000−22−22−22−2200000000000000000002−22−2−22−222−22−2000000
χ712-222-22-2-22200-22-22-22-222-22-2-20-20-2200-22002-20000000000002−22−22−22−20000000000000000000−22−22−22−222−22−2000000
χ722-222-22-2-22200-22-22-22-222-22-2-20-20-2200-22002-2000000000000−22−22−22−2200000000000000000002−22−22−22−2−22−22000000
χ732-222-22-2-2-2-2002-22-22-22-22-22-22020-2200-2200-22000000000000i2−i2i2−i2−i2i2−i2i20000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000
χ742-222-22-2-2-2-2002-22-22-22-22-22-22020-2200-2200-22000000000000−i2i2−i2i2i2−i2i2−i20000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000
χ752-222-22-2-2-2-2002-22-2-22-22-22-222020-22002-2002-2000000000000i2−i2i2−i2−i2i2−i2i20000000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000
χ762-222-22-2-2-2-2002-22-2-22-22-22-222020-22002-2002-2000000000000−i2i2−i2i2i2−i2i2−i20000000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000
χ772-222-22-2-2-2-200-22-222-22-2-22-2220202-200-22002-2000000000000i2−i2i2−i2−i2i2−i2i20000000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000
χ782-222-22-2-2-2-200-22-222-22-2-22-2220202-200-22002-2000000000000−i2i2−i2i2i2−i2i2−i20000000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000
χ792-222-22-2-2-2-200-22-22-22-222-22-220202-2002-200-22000000000000i2−i2i2−i2−i2i2−i2i20000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000
χ802-222-22-2-2-2-200-22-22-22-222-22-220202-2002-200-22000000000000−i2i2−i2i2i2−i2i2−i20000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000
χ81444-4-4-4-444-4-4400000000000044-4-4000000000000-4400000000000000000000000000000000000000000000000000000
χ82444-4-4-4-44-444-4000000000000-4-444000000000000-4400000000000000000000000000000000000000000000000000000
χ8344-4-4-444-4004-4000000000000040-40000000000000022−22−222222−22−2222000000000000000000000000000000000000000000000
χ8444-4-4-444-4004-4000000000000040-400000000000000−222222−22−222222−22000000000000000000000000000000000000000000000
χ8544-4-4-444-400-440000000000000-404000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000000
χ8644-4-4-444-400-440000000000000-40400000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000000
χ874-44-44-44-44-400000000000000-404000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000
χ884-44-44-44-44-400000000000000-40400000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000
χ894-44-44-44-4-440000000000000040-40000000000000000000000022−22−2222−222222−220000000000000000000000000000000000000
χ904-44-44-44-4-440000000000000040-400000000000000000000000−222222−2222−22−22220000000000000000000000000000000000000
χ914-4-44-4-44400004-4-444-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-44400004-4-44-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000000
χ934-4-44-4-4440000-444-44-4-44-444-400000000000000000000000000000000000000000000000000000000000000000000000
χ944-4-44-4-4440000-444-4-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000
χ958-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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