Finite Group Databasebeta

← Group #223178

Character table — Group #223178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11111111222222222222222222224444444444444444444444444444448888888888888888888888888888888161616161616
order12222222444444444444444444444444444444444488888888888888882244444888888888888888888888888444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
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
χ511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii111-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11-1-111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i111-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-1-111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-111-1-1
χ9111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ10111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ11111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111
χ12111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1111-1-1ii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11-1-111ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11-1-111−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1111-1-1−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i1-1-1-111
χ1711111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-11-11-1
χ1811111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-11111-11-11
χ1911111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-111-11-11
χ2011111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111111-1-111-1-111-1-111-1-111-1-11-11-1
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111iiii−i−i−i−iiiii−i−i−i−i1-1-111-1-1−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii-111-1-11
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-111−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-111-1
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-111ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-111-1
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111−i−i−i−iiiii−i−i−i−iiiii1-1-111-1-1ii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i-111-1-11
χ2511111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-111-1-11111111111111111-11-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-11-11
χ2611111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1111-11-1
χ2711111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111111-11-1
χ2811111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111111111-1-111-1-111-1-111-1-1-1-1-11-11
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-111iiii−i−i−i−iiiii−i−i−i−i-11-111-1-1−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i-11-111-1
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii-11-1-1-111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii1-11-1-11
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-1-1-111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i1-11-1-11
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-111−i−i−i−iiiii−i−i−i−iiiii-11-111-1-1ii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iii-11-111-1
χ33222222222222222222222-222-2-22-2-2-2-2-2-2-2-2-22222220000000000000000-2-2-20000000000000000000000000000000000
χ3422222222222222222222-22-2-222-22-2-2222222-2-2-2-2-2-20000000000000000-2-2-20000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-22-222-2-22-2-2-22222-2-2-2-2-2-222000000000000000022-20000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-22-2-222-22-2-2-2-2-2-2222222-2-2000000000000000022-20000000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-22-222-2-22-2-2-2-2-2222222-2-2-2-20000000000000000-2220000000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-22-2-222-22-2-222-2-2-2-2-2-222220000000000000000-2220000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222222-222-2-22-2-2-222-2-222-2-222-2-200000000000000002-220000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-22-2-222-22-2-2-2-222-2-222-2-22200000000000000002-220000000000000000000000000000000000
χ4122-22-2-2-2222-2-22i2i−2i−2i2i2i−2i−2i20-2-20020000000002i−2i2i−2i2-20000000022−2−222−2−2000000000002−22−200000000i2−i2i2−i2i2−i2i2−i2000000
χ4222-22-2-2-2222-2-22i2i−2i−2i2i2i−2i−2i20-2-20020000000002i−2i2i−2i2-200000000−2−222−2−22200000000000−22−2200000000−i2i2−i2i2−i2i2−i2i2000000
χ4322-22-2-2-2222-2-22i2i−2i−2i2i2i−2i−2i-202200-2000000000−2i2i−2i2i-2200000000i2i2−i2−i2−i2−i2i2i200000000000i2−i2−i2i200000000−22−222−22−2000000
χ4422-22-2-2-2222-2-22i2i−2i−2i2i2i−2i−2i-202200-2000000000−2i2i−2i2i-2200000000−i2−i2i2i2i2i2−i2−i200000000000−i2i2i2−i2000000002−22−2−22−22000000
χ4522-22-2-2-2222-2-2−2i−2i2i2i−2i−2i2i2i20-2-2002000000000−2i2i−2i2i2-20000000022−2−222−2−2000000000002−22−200000000−i2i2−i2i2−i2i2−i2i2000000
χ4622-22-2-2-2222-2-2−2i−2i2i2i−2i−2i2i2i20-2-2002000000000−2i2i−2i2i2-200000000−2−222−2−22200000000000−22−2200000000i2−i2i2−i2i2−i2i2−i2000000
χ4722-22-2-2-2222-2-2−2i−2i2i2i−2i−2i2i2i-202200-20000000002i−2i2i−2i-2200000000i2i2−i2−i2−i2−i2i2i200000000000i2−i2−i2i2000000002−22−2−22−22000000
χ4822-22-2-2-2222-2-2−2i−2i2i2i−2i−2i2i2i-202200-20000000002i−2i2i−2i-2200000000−i2−i2i2i2i2i2−i2−i200000000000−i2i2i2−i200000000−22−222−22−2000000
χ4922-22-2-2-22-2-2222i2i−2i−2i−2i−2i2i2i20-2-20020000000002i−2i−2i2i-220000000022−2−222−2−200000000000−22−2200000000i2−i2−i2i2i2−i2−i2i2000000
χ5022-22-2-2-22-2-2222i2i−2i−2i−2i−2i2i2i20-2-20020000000002i−2i−2i2i-2200000000−2−222−2−222000000000002−22−200000000−i2i2i2−i2−i2i2i2−i2000000
χ5122-22-2-2-22-2-2222i2i−2i−2i−2i−2i2i2i-202200-2000000000−2i2i2i−2i2-200000000i2i2−i2−i2−i2−i2i2i200000000000−i2i2i2−i200000000−222−22−2−22000000
χ5222-22-2-2-22-2-2222i2i−2i−2i−2i−2i2i2i-202200-2000000000−2i2i2i−2i2-200000000−i2−i2i2i2i2i2−i2−i200000000000i2−i2−i2i2000000002−2−22−222−2000000
χ5322-22-2-2-22-2-222−2i−2i2i2i2i2i−2i−2i20-2-2002000000000−2i2i2i−2i-220000000022−2−222−2−200000000000−22−2200000000−i2i2i2−i2−i2i2i2−i2000000
χ5422-22-2-2-22-2-222−2i−2i2i2i2i2i−2i−2i20-2-2002000000000−2i2i2i−2i-2200000000−2−222−2−222000000000002−22−200000000i2−i2−i2i2i2−i2−i2i2000000
χ5522-22-2-2-22-2-222−2i−2i2i2i2i2i−2i−2i-202200-20000000002i−2i−2i2i2-200000000i2i2−i2−i2−i2−i2i2i200000000000−i2i2i2−i2000000002−2−22−222−2000000
χ5622-22-2-2-22-2-222−2i−2i2i2i2i2i−2i−2i-202200-20000000002i−2i−2i2i2-200000000−i2−i2i2i2i2i2−i2−i200000000000i2−i2−i2i200000000−222−22−2−22000000
χ5722-2-2-222-22-22-22i−2i2i−2i2i−2i2i−2i0200-2-202002i−2i2i−2i2-2000000i2i2−i2−i2i2i2−i2−i2000000000000000i2−i2i2−i200002−22−22−22−200000000000000
χ5822-2-2-222-22-22-22i−2i2i−2i2i−2i2i−2i0200-2-202002i−2i2i−2i2-2000000−i2−i2i2i2−i2−i2i2i2000000000000000−i2i2−i2i20000−22−22−22−2200000000000000
χ5922-2-2-222-22-22-22i−2i2i−2i2i−2i2i−2i0-200220-200−2i2i−2i2i-2200000022−2−2−2−2220000000000000002−2−220000−i2i2−i2i2i2−i2i2−i200000000000000
χ6022-2-2-222-22-22-22i−2i2i−2i2i−2i2i−2i0-200220-200−2i2i−2i2i-22000000−2−22222−2−2000000000000000−222−20000i2−i2i2−i2−i2i2−i2i200000000000000
χ6122-2-2-222-22-22-2−2i2i−2i2i−2i2i−2i2i0200-2-20200−2i2i−2i2i2-2000000i2i2−i2−i2i2i2−i2−i2000000000000000i2−i2i2−i20000−22−22−22−2200000000000000
χ6222-2-2-222-22-22-2−2i2i−2i2i−2i2i−2i2i0200-2-20200−2i2i−2i2i2-2000000−i2−i2i2i2−i2−i2i2i2000000000000000−i2i2−i2i200002−22−22−22−200000000000000
χ6322-2-2-222-22-22-2−2i2i−2i2i−2i2i−2i2i0-200220-2002i−2i2i−2i-2200000022−2−2−2−2220000000000000002−2−220000i2−i2i2−i2−i2i2−i2i200000000000000
χ6422-2-2-222-22-22-2−2i2i−2i2i−2i2i−2i2i0-200220-2002i−2i2i−2i-22000000−2−22222−2−2000000000000000−222−20000−i2i2−i2i2i2−i2i2−i200000000000000
χ6522-2-2-222-2-22-222i−2i2i−2i−2i2i−2i2i0200-2-202002i−2i−2i2i-22000000i2i2−i2−i2i2i2−i2−i2000000000000000−i2i2−i2i200002−2−222−2−2200000000000000
χ6622-2-2-222-2-22-222i−2i2i−2i−2i2i−2i2i0200-2-202002i−2i−2i2i-22000000−i2−i2i2i2−i2−i2i2i2000000000000000i2−i2i2−i20000−222−2−222−200000000000000
χ6722-2-2-222-2-22-222i−2i2i−2i−2i2i−2i2i0-200220-200−2i2i2i−2i2-200000022−2−2−2−222000000000000000−222−20000−i2i2i2−i2i2−i2−i2i200000000000000
χ6822-2-2-222-2-22-222i−2i2i−2i−2i2i−2i2i0-200220-200−2i2i2i−2i2-2000000−2−22222−2−20000000000000002−2−220000i2−i2−i2i2−i2i2i2−i200000000000000
χ6922-2-2-222-2-22-22−2i2i−2i2i2i−2i2i−2i0200-2-20200−2i2i2i−2i-22000000i2i2−i2−i2i2i2−i2−i2000000000000000−i2i2−i2i20000−222−2−222−200000000000000
χ7022-2-2-222-2-22-22−2i2i−2i2i2i−2i2i−2i0200-2-20200−2i2i2i−2i-22000000−i2−i2i2i2−i2−i2i2i2000000000000000i2−i2i2−i200002−2−222−2−2200000000000000
χ7122-2-2-222-2-22-22−2i2i−2i2i2i−2i2i−2i0-200220-2002i−2i−2i2i2-200000022−2−2−2−222000000000000000−222−20000i2−i2−i2i2−i2i2i2−i200000000000000
χ7222-2-2-222-2-22-22−2i2i−2i2i2i−2i2i−2i0-200220-2002i−2i−2i2i2-2000000−2−22222−2−20000000000000002−2−220000−i2i2i2−i2i2−i2−i2i200000000000000
χ732-2-222-22-20000000000002-22-22-2-222-20000000000002i−2i2i−2i2i−2i2i−2i2-22-22-22-20002i−2i2i−2i000000000000000000000000000000
χ742-2-222-22-20000000000002-22-22-2-222-20000000000002i−2i2i−2i2i−2i2i−2i-22-22-22-22000−2i2i−2i2i000000000000000000000000000000
χ752-2-222-22-20000000000002-22-22-2-222-2000000000000−2i2i−2i2i−2i2i−2i2i2-22-22-22-2000−2i2i−2i2i000000000000000000000000000000
χ762-2-222-22-20000000000002-22-22-2-222-2000000000000−2i2i−2i2i−2i2i−2i2i-22-22-22-220002i−2i2i−2i000000000000000000000000000000
χ772-2-222-22-2000000000000-22-22-222-22-20000000000002-22-2-22-222i−2i2i−2i−2i2i−2i2i000−2i2i2i−2i000000000000000000000000000000
χ782-2-222-22-2000000000000-22-22-222-22-20000000000002-22-2-22-22−2i2i−2i2i2i−2i2i−2i0002i−2i−2i2i000000000000000000000000000000
χ792-2-222-22-2000000000000-22-22-222-22-2000000000000-22-222-22-22i−2i2i−2i−2i2i−2i2i0002i−2i−2i2i000000000000000000000000000000
χ802-2-222-22-2000000000000-22-22-222-22-2000000000000-22-222-22-2−2i2i−2i2i2i−2i2i−2i000−2i2i2i−2i000000000000000000000000000000
χ81444-44-4-4-44-4-444-4-444-4-44000000000000000000000000000000000000000000000000000000000000000000000000000
χ82444-44-4-4-44-4-44-444-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ83444-44-4-4-4-444-44-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ84444-44-4-4-4-444-4-444-44-4-44000000000000000000000000000000000000000000000000000000000000000000000000000
χ854-444-44-4-400000000000040-4400-40000000000000000000000022−22−222222−22−22220000000000000000000000000000000000000
χ864-444-44-4-400000000000040-4400-400000000000000000000000−222222−22−222222−220000000000000000000000000000000000000
χ874-444-44-4-4000000000000-404-4004000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000
χ884-444-44-4-4000000000000-404-400400000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000
χ894-44-4-4-44400000000000004004-40-4000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000000
χ904-44-4-4-44400000000000004004-40-400000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000000
χ914-44-4-4-4440000000000000-400-44040000000000000022−22−222222−22−2222000000000000000000000000000000000000000000000
χ924-44-4-4-4440000000000000-400-440400000000000000−222222−22−222222−22000000000000000000000000000000000000000000000
χ934-4-444-44-4000000000000444-4-44-4-4-4400000000000000000000000000000000000000000000000000000000000000000
χ944-4-444-44-4000000000000-4-4-444-444-4400000000000000000000000000000000000000000000000000000000000000000
χ958-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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